Mokrane Bala
email: mokrane.bala@imt-lille-douai.fr

Rachid Zentar

Pascal Boustingorry

Parameter determination of the Compressible Packing Model (CPM) for concrete application

Keywords:

The packing density of granular materials is in the centre of interest of many industries. For concrete industry, the packing density of aggregates is the most representative physical parameter of the granular mixtures: it combines the grain size and the morphology of grains. Compressible Packing Model (CPM) accurately predicts packing density by involving three parameters: wall effect coefficient, loosening effect coefficient and compaction index. The identification of these parameters has been made on elementary granular classes (narrow particle size distributions) which can be time consuming and difficult to achieve. In this research work, we have elaborate a strategy to determine CPM parameters for wide particle size distribution of granular mixtures. This allows reducing the number of tests to optimize packing density of granular mixtures. The results of the modelling show a good agreement with the experiment. The work will be undertaken on two typologies of grains: crushed and rolled aggregates.

Introduction

In the field of civil engineering, concrete is an indispensable raw material which often offering the best technical and economic choice for the construction of buildings and infrastructures. Aggregates in concrete reach up to 80% of the total volume and come in different sizes and shapes. The remaining volume is occupied by a cement paste. Aggregates can arise from natural, artificial or recycled (industrial by-product and demolition source materials). The most important property in the granular mixture of concrete is its packing density. Packing density optimization for the granular mixtures allows not only minimizing the quantity of cement incorporated in the concrete but also enhances its performance and durability [START_REF] Andersen | Particle packing and concrete properties[END_REF], [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF].

In conventional concrete mix design methods, granular mixtures are determined empirically, often from particle size distribution curves (ideal distribution curves), as for the works of Fuller & Thompson (1907), Andreasen & Andersen (1929), Faury (1958) and Dreux (1970) [START_REF] Roquier | Etude de la compacité optimale des mélanges granulaires binaires: classe granulaire dominante, effet de paroi, effet de desserrement[END_REF], [START_REF] Fennis | Using particle packing technology for sustainable concrete mixture design[END_REF]. These methods make it possible to determine the ideal proportions of each grain size to approach the maximum packing density of the mix, but do not allow to predict accurately the packing density [START_REF] Roquier | Etude de la compacité optimale des mélanges granulaires binaires: classe granulaire dominante, effet de paroi, effet de desserrement[END_REF] and may require several series of experiments for the optimization of the granular mix [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF].

With the emergence of modern concretes and special concretes in the 20th century (such as High Performance Concretes (HPC), Self-Compacting Concrete (SCC)…), concrete mix design by "ideal" particle size distribution curves proved to be difficult or unsuccessful [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF]. For these concretes, several objectives are aimed at the same time: obtaining high workability, without risk of segregation and good mechanical properties. Therefore, a wide variety of distributions are possible and there is no ideal curve that suits all requirements [START_REF] Roquier | Etude de la compacité optimale des mélanges granulaires binaires: classe granulaire dominante, effet de paroi, effet de desserrement[END_REF].

In order to appear to these difficulties, several models have been developed to predict the packing density of a granular mixture. Modelling of packing density was developed first by highlighting the interaction effects between grains of different sizes, in particular by the work of Caquot (1937), which shows the major influence of the wall effect on granular mixtures [START_REF] Roquier | Etude de la compacité optimale des mélanges granulaires binaires: classe granulaire dominante, effet de paroi, effet de desserrement[END_REF]. It has prompted researchers to study granular classes in pairs. Inspired by Mooney viscosity model (1950), Stovall studied binary mixtures, with and without interaction. He has developed the linear packing model [START_REF] Stovall | Linear packing density model of grain mixtures[END_REF] for granular mixtures with multiple classes, taking into account both the wall effects and the loosening effect between the granular classes of different sizes. The loosening effect appears when a small grain is inserted in a dominant large grains population and the wall effect appears when some quantities of large grains isolated are immersed in fine grains agglomerate [START_REF] Miraoui | Road material basis in dredged sediment and basic oxygen furnace steel slag[END_REF].

The linear packing model was refined to build the virtual packing model that predicted virtual packing density (i.e. an orderly packing of grains with the least voids), including mixtures of grains of the same size but of different shapes. The virtual packing density for a mixture of "n" granular fractions where the class (i) is dominant, is given by Equation 1 [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF]. It involves the volume proportions of each of the granular classes (yi), their packing density when they are arranged separately (βi), the loosening effect coefficient (aij) given by Equation 2 and the wall effect coefficient (bji) given by Equation 3 [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF]. "e" is the void ratio of the granular mixture defined as the ratio of void and solid fraction (given by Equation 4, ∅ is the solid fraction).

= = ∑ ∑ Equation 1 Accepted Manuscript a = β ! ! "# + % & Equation 2 b = ( ! ) *+ *, ! ) , ! ( & Equation 3 -= ∅ ∅ Equation 4
A first attempt to predict the packing density by the Solid Suspension Model [START_REF] Sedran | Prévision de la compacité des mélanges granulaires par le modèle de suspension solide -I-Fondements théoriques et étalonnage du modèle[END_REF], [START_REF] Sedran | Prévision de la compacité des mélanges granulaires par le modèle de suspension solide -II-Validation, cas des mélanges confinés[END_REF] was limited by two defects related to the notion of reference viscosity (considered as a description of the degree of compaction of the system) and the interaction functions that were not satisfactory in their mathematical form [START_REF] De Larrard | Une nouvelle approche de la formulation des bétons[END_REF]. This compaction energy was introduced later in CPM model by the concept of the compaction index "K". This model makes it possible to predict the real packing density of a mixture of several granular classes from the knowledge of the compactness of each one-dimensional class and the energy of the setting up. The real packing density depends on the compaction energy. The real packing density "C" of a mixture of aggregates is connected to "K" by the expression given in Equation 5. Moreover, simplified formulas (Equation 6 and Equation 7) of the granular interaction coefficients (a and b) was proposed by de Larrard [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF] In the framework of the CPM, the prediction of the packing density is therefore possible after determination of the coefficients a, b (by the calculation of the void index at the limits of coarse grains dominant and fine grains dominant) and K. These parameters are calibrated on binary mixtures of aggregates of different natures (crushed and rolled) [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF], [START_REF] Lecomte | Modèle de suspension solide et formulation de bétons calcaires en Lorraine[END_REF]. The error between measured and calculated packing densities after calibration does not exceed 0.77% for rolled aggregates and 1.71% for crushed aggregates [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF].

In order to improve the prediction of the packing density, several models and calculation approaches have been proposed [START_REF] Toufar | Contribution of optimisation of components of different density in polydispersed particles systems[END_REF]- [START_REF] Roquier | A Theoretical Packing Density Model (TPDM) for ordered and disordered packings[END_REF]. Some authors introduced new interaction parameters [START_REF] Kwan | A 3-parameter particle packing model incorporating the wedging effect[END_REF], [START_REF] Roquier | The 4-parameter Compressible Packing Model (CPM) including a new theory about wall effect and loosening effect for spheres[END_REF].

Roquier [START_REF] Roquier | The 4-parameter Compressible Packing Model (CPM) including a new theory about wall effect and loosening effect for spheres[END_REF] introduced the interference effect that occurs when coarse grains, in a growing number, become too close to each other by trapping some fine grains in small spaces between them [START_REF] Roquier | Etude de la compacité optimale des mélanges granulaires binaires: classe granulaire dominante, effet de paroi, effet de desserrement[END_REF], [START_REF] Roquier | The 4-parameter Compressible Packing Model (CPM) including a new theory about wall effect and loosening effect for spheres[END_REF].

However, despite these various attempts to improve the packing density prediction, the CPM remains among the most accurate models and the most simplest to apply [START_REF] Moutassem | Assessment of Packing Density Models and Optimizing Concrete Mixtures[END_REF], [START_REF] Jones | Comparison of particle packing models for proportioning concrete constitutents for minimum voids ratio[END_REF]. Moutassem [START_REF] Moutassem | Assessment of Packing Density Models and Optimizing Concrete Mixtures[END_REF] had compared 9 packing density models and he found that the CPM predict correctly the packing density of granular mixtures used in concrete.

Other research works has focused on the CPM parameters in order to propose optimized values for aij, bji and K [START_REF] Lecomte | Modèle de suspension solide et formulation de bétons calcaires en Lorraine[END_REF], [START_REF] Jones | Comparison of particle packing models for proportioning concrete constitutents for minimum voids ratio[END_REF]. The work of Lecomte [START_REF] Lecomte | Modèle de suspension solide et formulation de bétons calcaires en Lorraine[END_REF] has slightly improved the calculation of the interaction coefficients through new simplified formulas of calculation. Indeed, the simplified formulas of the interaction coefficients are probably valid only for one type of aggregates which justifies the differences between the formulas proposed by de Larrard [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF] and by Lecomte [START_REF] Lecomte | Modèle de suspension solide et formulation de bétons calcaires en Lorraine[END_REF]. In fact, for the CPM, the functions of aij and bji have been calibrated on elementary granular classes (d and D are the minimum and maximum grain sizes respectively) while respecting on the one hand a ratio di/Di>0.1 (so that the elementary granular classes are the more unimodal possible) [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF] and on the other hand a ratio di/dj<4 [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF]. In the case of granular mixtures optimization for concrete, this work is long and expensive to achieve because it requires a long process of material preparation and sieving elementary granular classes.

In the present paper we will calibrate the CPM parameters in the case of large granular classes with di/Di<0.1 (especially for sand) and for some ratios dj/di>4. This study does not require any sieving work to obtain elementary granular classes that must have narrower particle size distributions. Our goal is to save time and materials in packing density studies of granular mixtures for concrete without affecting the accuracy of the model. First, we will apply the CPM as developed by de Larrard in order to qualify the prediction of the model and determine the most influential parameters. After that, we will optimize the parameters of the CPM for wide particle size distributions of granular mixtures of crushed and rolled aggregates. The coefficients a, b and K will be calibrated on binary mixtures. Finally, we will evaluate the accuracy of the model applied to large granular classes of binary and ternary mixtures compared to previous studies.

Materials and methods

In Table 1 are listed the aggregates of the present study and few characteristics. The size, shape and roughness of the grains are the three main parameters that affect the packing density [START_REF] Roquier | Etude de la compacité optimale des mélanges granulaires binaires: classe granulaire dominante, effet de paroi, effet de desserrement[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF], [START_REF] Lecomte | Compacité des mélanges et propriétés des grains[END_REF] that has influenced our choice. Rolled aggregates come from "Chevrières" quarry ("Hauts-de-France" region) and "Decize" quarry ("Bourgogne-Franche-Comté" region). The crushed aggregates come from the quarries of "Boulonnais" ("Nord Pas-de-Calais" region). The granular fractions adopted for this study range from sand (0/4 mm) to gravel (4/10 and 10/20 mm). The absolute density of the aggregates was measured according to the European standard NF EN 1097-6 [START_REF] Afnor | Tests for mechanical and physical properties of aggregates -Part 6: determination of particle density and water absorption[END_REF] and the particle size analysis was carried out according to the European standard NF EN 933-1 [START_REF] Afnor | Tests for geometrical properties of aggregates -Part 1: determination of particle size distribution -Sieving method[END_REF].

In order to measure the packing density of the mono-granular classes, the LPC procedure No. 61 was followed [START_REF] Ledee | Essai de compacité des fractions granulaires à la table à secousses: Mode opératoire[END_REF]. After weighing 7 kg of one mono-granular material, the sample is placed in a cylindrical mould in three equivalent layers. Each layer is subjected to 20 shocks in the shaking table before putting the next layer. The sample is then subjected to 40 shocks under a pressure of 10 kPa (equivalent weight of 20 kg can be placed above the sample). The energy transmitted by the shocks allows the granular material to be into a more dense configuration, which improves its packing density.

The compaction index (K) of this process was calibrated after several tests. Using Equation 5, K = 9 was found [START_REF] Ledee | Essai de compacité des fractions granulaires à la table à secousses: Mode opératoire[END_REF].

The packing densities were measured on binary granular mixtures of crushed and rolled aggregates to determine the interaction coefficients for each type of aggregates [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] Lecomte | Modèle de suspension solide et formulation de bétons calcaires en Lorraine[END_REF]. Different combinations between sand and gravels were analysed. As shown in Table 2, considering the maximum nominal diameter of each class, the effect of the size ratio D1/D2 and the grain shape on the packing density was experienced. Otherwise, the variation of the proportions of the smaller granular class in the binary mixture equal to 5% in the extreme parts of the curve of packing density and to 10% in the centre of the curve. This is in order to measure the impact of the granular interaction effects that have defined previously (wall effect and loosening effect coefficients). Finally, packing density of ternary granular mixtures was measured for crushed and rolled aggregates. This is in order to evaluate the efficiency of the interaction parameters determined on the binary mixtures. The measurements were realized by increment of 10%. The different combinations of the experimental program on ternary mixtures are shown in Fig. 1.

Results and discussions

The main properties of the aggregates used in this study are listed in Table 3. Otherwise, the particle size distribution of the different materials are shown in Fig. 2. Particle size analysis showed a high fines content in crushed sand (5% of grains are smaller than 63 microns and 16% smaller than 125 microns).

Packing densities measurement tests were realised using the compaction table according to LPC procedure No. 61 [START_REF] Ledee | Essai de compacité des fractions granulaires à la table à secousses: Mode opératoire[END_REF] on binary and ternary mixtures of crushed and rolled aggregates. The different materials are used in their raw state without any prior sieving to remove the fine fraction. For each test, two different measurements of compactness were made. In each case, the average packing density and the variances are calculated. It has been observed through the experimental program that the repeatability of the tests is ensured [START_REF] Bala | Parameter analysis of the compressible packing model for Concrete application[END_REF] (maximum standard deviation recorded is 0.017 for crushed aggregates and 0.008 for rolled aggregates). The use of the aggregates in their raw state without any prior sieving (fine particles content up to 7%) did not influence the packing density measurements by compaction table [START_REF] Bala | Parameter analysis of the compressible packing model for Concrete application[END_REF].

The evolution curves of the packing density measured by the compaction table as a function of the proportion of the addition of fine material are shown in Fig. 3. From the curves in Fig. 3, it is observed a rapid increase of the packing density when the sizes ratio of the mixed materials is large (D1/D2 = 5).

The packing density curves exhibits an optimum before decreasing when wall effects occur in the area where the small grains material becomes dominant. Even for smaller ratio (D1/D2=2.5), the evolution of the packing density still important (Fig. 3-b). For D1/D2=2, the packing density curve evolution is almost nil (Fig. 3-c). These results show that the packing density optimum of the binary mixtures increases when D1/D2 ratio increases from 2 up to 5. This is in agreement with the results found by de Larrard [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF] and McGeary [START_REF] Mcgeary | Mechanical packing of spherical particles[END_REF]. Finally, the size ratio D1/D2=2 seems to define the limit for materials which are in total interaction [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF].

Despite their low fines content, the rolled aggregates (Fig. 3. right) reaches the highest packing density in comparison to crushed aggregates. The packing of rolled aggregates is composed of grains of various sizes (wide particle size distribution) that their shape is close to the sphere. This packing approaches the Apollonian packing (packing of circles) which gives the highest packing density [START_REF] Delaney | Relation between grain shape and fractal properties in random Apollonian packing with grain rotation[END_REF], [START_REF] Weaire | The pursuit of perfect packing[END_REF]. The high fines content (particle content <63 microns) in the crushed aggregates (Fig. 3. left) was not able to counterbalance the shape effects in terms of packing density (Fig. 3a and Fig. 3b).

From these results, we deduce that the maximum packing density that can be achieved on binary mixtures is influenced by the combination of the following parameters (regardless of the compaction index): the packing density of the elementary granular classes, the shape and roughness of the grains as well as the fines content and the size ratio. The packing density of binary mixtures can be increased by improving the packing density of the elementary classes as found by de Larrad [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF].

Similarly, some authors have shown that the packing density increases when the size ratio of elementary classes increases [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] Roquier | The 4-parameter Compressible Packing Model (CPM) including a new theory about wall effect and loosening effect for spheres[END_REF], [START_REF] Yu | Porosity calculations of multi-component mixtures of spherical particles[END_REF]. The effect of the presence of ultra-fine particles (powders) can also be related to the large size ratio between the powders and coarse grains. between these materials as seen in Fig. 3-c.

The evolution curves of the experimental packing density for binary and ternary mixtures allow to proceed to the modelling of these packing densities by the CPM in which we will analyse the different parameters of the model which are: the coefficients of granular interactions (aij and bji) and the compaction index (K). This work will be undertaken for large granular classes.

In order to determine the packing densities by the CPM, the virtual packing densities are calculated using Equation 1where the coefficient of loosening effect (aij) and wall effect (bji) have to be determined. In the first method, these parameters are calculated using the simplified formulas (Equation 6 and Equation 7) proposed by de Larard [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF]. The real packing density of the mixtures is subsequently calculated through the compaction index which is taken equal to 9 [START_REF] Ledee | Essai de compacité des fractions granulaires à la table à secousses: Mode opératoire[END_REF]. In the second method and for comparison, the parameters aij and bji are determined on the experimental curves and the compaction index value is maintained equal to 9 as in the first method.

The results in terms of experimental data in comparison to the model prediction following the first method are shown in Fig. 5.

In this case the CPM allows to predict experimental packing densities with an average error of 3.2% for crushed aggregates and 1.7% for rolled aggregates. We note through the curves shown in Fig. 5 that the largest differences are found in the area of optimal packing density. In this zone, the packing density is overestimated by the CPM for crushed aggregate mixtures and underestimated in the case of rolled aggregate mixtures. This leads to say that the efficiency of the compaction mode by the compaction table is influenced not only by the particle size as found by Sadok et al. [START_REF] Sadok | Genetic programming for granular compactness modelling[END_REF], [START_REF] Abdelfeteh | Formulation de matériaux de construction à base de sous-produits industriels avec des méthodes issues de l'intelligence artificielle[END_REF], but also by the shape of the grains. The parameters a, b and K used in this first modelling are given in Table 4.

In the previous studies performed by de Larrard, an average error of 1.71% for crushed aggregates and 0.77% for rolled aggregates is found [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF].

In the second method, the parameters of the CPM are determined from experimental data. According to the basic formulas of interaction coefficients (Equation 2 and Equation 3), it could be seen that the slope of the experimental data in terms of void ratio (given by Equation 4) versus the percentage of fine material at the origin of the curve and at the extremity of the curve are respectively proportional to the parameters aij and bji. These latter are calculated using Equation 6 and Equation 7 after calculating A , A < and A B by Equation 5(K is taken equal to 9) and evaluating graphically the slope of the curve evolution of the void ratio as a function of the percentage of fine grains. The parameter determination for binary mixtures is highlighted in Fig. 6.

As it could be seen in Fig. 6, due to the discrepancy of the data, for some curves it is difficult to define the slope at the origin or at the extremity of the curve. In this order, the slope is evaluated on 25% of the curve (at the origin and at the extremity) in area considered as linear part. The values of the coefficients aij and bji determined (given in Table 5) were compared to those obtained by de Larrard [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF] and Lecomte [START_REF] Lecomte | Modèle de suspension solide et formulation de bétons calcaires en Lorraine[END_REF] as shown on Fig. 7. The results of the modelling are presented in Fig. 8.

As shown in Fig. 7, the coefficients aij and bji obtained on large granular classes follow the same evolution as those obtained by de Larrard [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF] and Lecomte [START_REF] Lecomte | Modèle de suspension solide et formulation de bétons calcaires en Lorraine[END_REF]. They increase when the ratio D2/D1 increases. This shows that the granular interactions are stronger when the granular classes are of the same size (until total interaction as shown in Fig. 3-c). However, Fig. 7 shows some differences between the interaction coefficients determined experimentally and the functions of the simplified formulas proposed by de Larrard or Lecompte. This allows to say that there is no unique function which makes it possible to calculate the interaction coefficients accurately for different type of aggregates and without causing errors in the prediction of the packing density. Moreover, when we analyse in more details the obtained results from our experimental data we can point out that the values of aij measured on rolled aggregates are systematically lower than those measured on crushed aggregates. This result could be observed for most data published by de Larard and is in line with the published paper of Roquier [START_REF] Roquier | A Theoretical Packing Density Model (TPDM) for ordered and disordered packings[END_REF]. In this later, the estimates of the loosening effect parameter calculated from two different models (4-parameter CPM as 3PPM) show clearly that the values calculated on rolled aggregates are lower than those calculated for crushed aggregates. It is also interesting to note that for small diameter ratios (D2/D1), the loosening effect parameter evolves very quickly with increasing the diameter ratios.

For the wall effects parameter bji, in terms of aggregates shape effects, the same conclusions than those addressed for the loosening effect parameter could be drawn. The measured parameters values on rolled aggregates are systematically lower than those measured on crushed aggregates. This is also in line with most published data from de Larrad and other researchers.

The comparisons of absolute values of the wall effect parameter seems to be systematically lower that the values of the loosening effect parameter in the whole range of the diameter ratios.

Finally the comparison of the measured values for both parameters with the calculated values using the proposed relationships by de Larrard [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF] and Lecomte [START_REF] Lecomte | Modèle de suspension solide et formulation de bétons calcaires en Lorraine[END_REF] shows that a big differences could be induced.

Comparisons between the predictions using CPM with identified aij and bji on experimental data and experimental results (Fig. 8) show better agreement than in the first method (modelling through simplified formulas of aij and bji). The difference between the model prediction and the experimental data decreases to 2.0% for crushed aggregates and 1.1% for rolled aggregates. These errors are similar to those found in the work by de Larrard [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF]. From these results, we can deduce that identification on elementary granular classes obtained by sieving is unnecessary to achieve the best performances of the CPM. However, it seems necessary to define interaction coefficients on experimental data.

In order to assess the effect of the compaction index (K) on the prediction of the CPM, in the last section of this study a back calculation of K on experimental data is undertaken. In this procedure, the difference between the model prediction and the experimental data is decreased by changing the value of K. The parameters aij and bji are kept as defined in the second method. The obtained results in terms of compaction index and errors between experimental data and prediction of the model is summarised in Table 6 and Fig. 9.

The compaction index obtained after calibration is lower than 9 (especially for crushed aggregates).

Different values of the compaction index are obtained (given in Table 6) depending on the granular mixture. The compaction index depends to the experimental process, other values of K was recorded with others experimental processes [START_REF] Sadok | Modélisation de la compacité granulaire par une approche d'Apprentissage Automatique[END_REF], [START_REF] Thanh | Valorisation de sédiments marins et fluviaux en technique routière[END_REF]. But for compaction mode by shaking table, K must be constant because the energy used was constant [START_REF] Miraoui | Road material basis in dredged sediment and basic oxygen furnace steel slag[END_REF]. We conclude that for crushed aggregates the compaction by the shaking table is not effective [START_REF] Bala | Parameter analysis of the compressible packing model for Concrete application[END_REF], [START_REF] Bala | Etude d'impact de la forme des granulats sur les paramètres du modèle d'empilement compressible[END_REF]. This is due to their high fines content [START_REF] De Larrard | Structures granulaires et formulation des bétons[END_REF], [START_REF] Abdelfeteh | Formulation de matériaux de construction à base de sous-produits industriels avec des méthodes issues de l'intelligence artificielle[END_REF]. With regard to the rolled aggregates, the compaction efficiency was better since we could reach a compaction index close to 9. However, the difference is not very significant in terms of packing density prediction, from which we retain the compaction index K = 9 for modelling of ternary mixtures.

In the case of ternary mixtures, the prediction of the experimental data is undertaken using CPM with aij and bji as defined in method 2 on binary mixtures. The compaction index, following the observed results on the binary mixtures and the results of several authors [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] Roquier | Etude de la compacité optimale des mélanges granulaires binaires: classe granulaire dominante, effet de paroi, effet de desserrement[END_REF], [START_REF] Abdelfeteh | Formulation de matériaux de construction à base de sous-produits industriels avec des méthodes issues de l'intelligence artificielle[END_REF] the result is value is fixed to 9. To ease the comparisons, the predicted results versus experiments are shown on Fig. 10.

The errors observed between the model and the experiments for ternary mixtures is about 2.4% for crushed aggregates and 1.6% for rolled aggregates. From the results shown on Fig. 10, we note that in the majority of ternary mixtures of crushed and rolled aggregates, CPM overestimates the packing density.

Conclusion and perspectives

In this paper, the prediction of packing density of binary and ternary mixtures of crushed and rolled aggregates was investigated. From this study, we can draw the following conclusions:

-For packing density measurements at the compaction table made with materials including the fine fraction (<63 microns), the repeatability of the tests is ensured (maximum standard deviation of 0.015 between two tests). The segregation effects of fine particles can be neglected for crushed and rolled aggregates with fine particles (less than 63 microns) content up to 7%.

-The modelling of the packing density by the CPM have shown that the use of the granular interaction coefficients determined by the simplified formulas is insufficient to have a good prediction.

-The back calculation of the compaction index (K) may vary from one mixture to another (especially for crushed aggregates).

-It has been demonstrated in this study that the CPM can be applied to large granular classes without creating elementary subclasses. This save time and materials in packing density studies, especially for concrete mix design.

-The identification of the model coefficients following the procedure suggested improved the prediction of the CPM.

The experimental program and the modelization realized allow to improve the precision of the CPM in the determination of the packing density of granular mixtures for concrete. In the perspective of this study, the packing density will be exploited to go back to the yield stress and the compressive strength of concrete following the approaches of Chateau et al. [START_REF] Chateau | Homogenization approach to the behavior of suspensions of noncolloidal particles in yield stress fluids[END_REF] and de Larrard [START_REF] De Larrard | Concrete mixture proportioning: a scientific approach[END_REF], [START_REF] De Larrard | L'influence du granulat sur la résistance à la compression des bétons[END_REF] respectevly by combining the results of this study with the study of the properties of the cement paste.

  after calibration of the CPM on different series of experimental data.

For

  the ternary mixtures (of crushed aggregates) studied in this research work, the results are shown in Fig. 4. The packing density measured decreases in the area of low sand content (dark area) and increases with the introduction of sand (white area). The presence of intermediate gravel (G 4/10) with the coarser gravel (G 10/20) disturbs the granular mixture because of the observed interaction

Fig. 1 :Fig. 2 :Fig. 3 :Fig. 4 :Fig. 5 :Fig. 7 :Fig. 8 :Fig. 9 :Fig. 10 :

 1234578910 Fig. 1: Experimental program of ternary mixtures (Crushed aggregates)

Table 4 : Parameters used for modelling by simplified formulas of a and b (K = 9)

 4

	Type of aggregates	D1	D2	Mixtures	D2/D1	a & b by simplified formulas a b K Average error
		10	4	SC 0/4 + GC 4/10	0.40	0.64	0.54		1.5%
		20	4	SC 0/4 + GC 10/20	0.20	0.45	0.28	9	2.8%
	Crushed	20	10	GC 4/10 + GC 10/20	0.50	0.71	0.65		5.2%
					Average error for crushed aggregates		3.2%
		10	4	SR + GR 4/10	0.40	0.64	0.54		2.2%
	Rolled	22 22	4 10	SR + GR 10/20 GR 4/10 + GR 10/20	0.18 0.45	0.43 0.68	0.26 0.60	9	2.1% 0.7%
					Average error for rolled aggregates		1.7%

Table 5 : Parameters of the modelling by calibrated formulas of a and b (K = 9)

 5

	Type of aggregates	D1	D2	Mixtures	D2/D1	a	a & b after calibration b K Average error
		10	4	SC 0/4 + GC 4/10	0.40	0.62	0.22		1.1%
	Crushed	20 20	4 10	SC 0/4 + GC 10/20 GC 4/10 + GC 10/20	0.20 0.50	0.54 0.90	0.30 0.83	9	2.1% 2.9%
					Average error for crushed aggregates		2.0%
		10	4	SR + GR 4/10	0.40	0.53	0.06		1.2%
	Rolled	22 22	4 10	SR + GR 10/20 GR 4/10 + GR 10/20	0.18 0.45	0.32 0.87	0.01 0.71	9	0.6% 1.4%
					Average error for rolled aggregates		1.1%

Table 6 : Parameters of the modelling after calibration of a, b and K

 6

	Type of aggregates	D1	D2	Mixtures	D2/D1	a	a, b and K after calibration b Average K error
		10	4	SC 0/4 + GC 4/10	0.40	0.62	0.22	5.5	0.8%
		20	4	SC 0/4 + GC 10/20	0.20	0.54	0.30	3.2	1.1%
	Crushed	20	10	GC 4/10 + GC 10/20	0.50	0.90	0.83	0.3	1.1%
					Average error for crushed aggregates		1.0%
		10	4	SR + GR 4/10	0.40	0.53	0.06	4.8	0.8%
		22	4	SR + GR 10/20	0.18	0.32	0.01	8.2	0.6%
	Rolled	22	10	GR 4/10 + GR 10/20	0.45	0.87	0.71	2.0	0.7%
					Average error for rolled aggregates		0.7%

Acknowledgements

The authors thank the R & D department of CHRYSO France for their technical and financial support for this research work.


The goal of query optimization in query federation over linked data is to minimize the response time and the completion time. Communication time has the highest impact on them both. Static query optimization can end up with inefficient execution plans due to unpredictable data arrival rates and missing statistics. This study is an extension of adaptive join operator which always begins with symmetric hash join to minimize the response time, and can change the join method to bind join to minimize the completion time. The authors extend adaptive join operator with bind-bloom join to further reduce the communication time and, consequently, to minimize the completion time. They compare the new operator with symmetric hash join, bind join, bind-bloom join, and adaptive join operator with respect to the response time and the completion time. Performance evaluation shows that the extended operator provides optimal response time and further reduces the completion time. Moreover, it has the adaptation ability to different data arrival rates.

As the increase in the number of data sources on linked data, a distributed data space on the web is generated. This huge global data space can be automatically queried by using two approaches called link traversal [START_REF] Hartig | Executing SPARQL Queries over the Web of Linked Data[END_REF] and query federation (Görlitz & Staab, 2011a). The first approach is based on discovering potentially relevant data by following the links between them. In other words, it finds the related data sources during the query execution. The second approach, query federation, divides the query into subqueries and distributes them to the SPARQL endpoints of the relevant data sources. The intermediate results from the data sources are aggregated and the final results are generated. Although both approaches have the advantage of providing up-to-date results, link traversal cannot guarantee finding all results because the relevant data sources change according to the starting point. For this reason, we focus on the query federation approach.

The objective of engines in query federation is to minimize both the response time and the completion time. Response time is the time to generate the first result tuple, whereas completion time is the time to provide all result tuples. Response time and completion time include communication time, I/O time and CPU time. Since the communication time dominates other costs, the main objective of the federated query engines can be stated as to minimize the communication cost. Static query optimization [START_REF] Selinger | Access Path Selection in a Relational Database Management System[END_REF] is not adequate for federated queries, because they are executed over the SPARQL endpoints of the selected distributed data sources on the web, and the data arrival rates are unexpected. Moreover, most of the statistics about the data sources are missing or unreliable. These constraints show that adaptive query optimization [START_REF] Deshpande | Adaptive Query Processing[END_REF]) is a necessity for query federation over linked data.

Adaptive query optimization has been studied in detail in relational databases [START_REF] Babu | Adaptive Query Processing in the Looking Glass[END_REF][START_REF] Deshpande | Adaptive Query Processing[END_REF][START_REF] Morvan | Dynamic Query Optimisation: Towards Decentralised Methods[END_REF][START_REF] Gounaris | Adaptive Query Processing in Distributed Settings[END_REF]. However, it is a new research area for linked data. There are only two engines which consider adaptive query optimization for federated queries over SPARQL endpoints: ANAPSID [START_REF] Acosta | ANAPSID: An Adaptive Query Processing Engine for SPARQL Endpoints[END_REF] and ADERIS [START_REF] Lynden | Adaptive Integration of Distributed Semantic Web Data[END_REF], 2011). The first one proposes a non-blocking join method based on symmetric hash join [START_REF] Wilschut | Dataflow Query Execution in a Parallel Main-Memory Environment[END_REF] and Xjoin [START_REF] Urhan | XJoin: A Reactively-Scheduled Pipelined Join Operator[END_REF], while the second one uses a cost model for dynamically changing the join order. Other than these, AVALANCHE [START_REF] Basca | Avalanche: Putting the Spirit of the Web back into Semantic Web Querying[END_REF][START_REF] Basca | Querying a messy web of data with Avalanche[END_REF] collects statistical information about relevant data sources and then generates its execution plan to provide the first k tuples. In addition, there are several studies which concentrate on join ordering for SPARQL queries by using different techniques such as evolutionary algorithms [START_REF] Oren | Anytime Query Answering in RDF Through Evolutionary Algorithms[END_REF][START_REF] Hogenboom | RCQ-GA: RDF Chain Query Optimization Using Genetic Algorithms[END_REF] and ant colony [START_REF] Hogenboom | Ant colony optimization for {RDF} chain queries for decision support[END_REF][START_REF] Kalayci | An ant colony optimisation approach for optimising SPARQL queries by reordering triple patterns[END_REF]. To the best of our knowledge, adaptive join operator [START_REF] Oguz | Adaptive Join Operator for Federated Queries over Linked Data Endpoints[END_REF] is the first study which aims to reduce both the response time and the completion time for query federation over SPARQL endpoints.

As mentioned above, the communication cost is the dominant cost in distributed environments. Bloom filter [START_REF] Bloom | Space/Time Trade-offs in Hash Coding with Allowable Errors[END_REF], which is a space efficient data structure, is widely used in relational databases [START_REF] Mackert | R* Optimizer Validation and Performance Evaluation for Local Queries[END_REF][START_REF] Mullin | Optimal semijoins for distributed database systems[END_REF][START_REF] Michael | Improving distributed join efficiency with extended bloom filter operations[END_REF][START_REF] Ives | Sideways Information Passing for Push-Style Query Processing[END_REF]. It is utilized in different linked data tasks such as identity reasoning [START_REF] Williams | Supporting identity reasoning in SPARQL using bloom filters[END_REF] and data source selection [START_REF] Hose | Towards Benefit-based RDF Source Selection for SPARQL Queries[END_REF]. Bloom filter is also employed to reduce the communication cost in two studies of linked data [START_REF] Basca | Querying a messy web of data with Avalanche[END_REF][START_REF] Groppe | Distributed join approaches for W3C-conform SPARQL endpoints[END_REF].

In this paper, we present an extended version of our previous work [START_REF] Oguz | Adaptive Join Operator for Federated Queries over Linked Data Endpoints[END_REF] in which adaptive join operator is proposed. The new contributions of this paper are as follows: i) We improve our previous proposal with bind-bloom join [START_REF] Basca | Querying a messy web of data with Avalanche[END_REF][START_REF] Groppe | Distributed join approaches for W3C-conform SPARQL endpoints[END_REF] for both single join queries and multi-join queries by including bind-bloom join to the candidate join methods. ii) We present a detailed performance evaluation study which shows the advantage of our new proposal. iii) We extend our related work with new studies and comparison of adaptive query optimization methods in query federation. Our operator uses symmetric hash join in the beginning to minimize the response time, and can change the join method to bind join or bind-bloom join. Bind-bloom join, shortly can be defined as a kind of bind join enhanced with bloom filter in order to minimize the communication time. It is explained in detail in the following section. Performance evaluation shows that the extended operator has both the advantage of optimal response time and the adaptation ability to different data arrival rates in order to minimize the completion time. Moreover, it provides faster completion time than our previous operator in all test cases. The rest of the paper is organized as follows: Section 2 introduces our approach for both single join queries and multi-join queries. Section 3 presents the results and discussions on performance evaluation. Section 4 covers the related work and Section 5 concludes the paper.

In our previous work [START_REF] Oguz | Adaptive Join Operator for Federated Queries over Linked Data Endpoints[END_REF], we have proposed an adaptive join operator for federated queries over linked data endpoints, called AJO. It always begins with symmetric hash join in order to minimize the response time, and when all the tuples of a relation arrive, it estimates the remaining times for symmetric hash join and bind join in order to minimize the completion time. It changes the join method to bind join if it estimates that it is more efficient than symmetric hash join. In this paper, we propose an extended version of AJO with bind-bloom join in order to further reduce the communication time. In this section, we first explain the principles of symmetric hash join, bind join, bloom filter, and bind-bloom join. Second, we present our proposal for single join queries and multi-join queries.

Symmetric hash join [START_REF] Wilschut | Dataflow Query Execution in a Parallel Main-Memory Environment[END_REF] maintains a hash table for each relation. Thus, it is a non-blocking join method which produces the first result tuple as early as possible. In other words, it is good at response time. Bind join [START_REF] Haas | Optimizing Queries Across Diverse Data Sources[END_REF], which is the most popular join method among the federated query engines [START_REF] Oguz | Federated query processing on linked data: A qualitative survey and open challenges[END_REF], passes the bindings of the intermediate results of the outer relation to the inner relation to filter the result set. It provides good completion time when the cardinalities of the first relation and the intermediate results are low. Equation 1and Equation 2show the cost functions of these join methods that are the variations of the formulas in [START_REF] Quilitz | Querying Distributed RDF Data Sources with SPARQL[END_REF]. R1 and R2 are relations, card(R) is the number of tuples in R, c t R is the transfer cost of R for one result tuple, and R2 is the relation with the bindings of R1:

cost R ( ⋈ SHJ t t R card R c card R c R R 2 1 2 1 2 ) = ( ) ⋅ + ( ) ⋅ (1) cost R ( ⋈ BJ t t t R card R c card R c card R c R R R 2 1 1 2 1 2 2 ) = ( ) ⋅ + ( ) ⋅ + ( ) ⋅ ' (2)
Bloom filter [START_REF] Bloom | Space/Time Trade-offs in Hash Coding with Allowable Errors[END_REF] is a data structure which represents a set of elements in a bit vector with a low rate of false positives. The idea is to represent a set S = {e 1 , e 2 , e 3 , . . ., e n } of n elements in a vector v of m bits. Initially all the bits are set to 0. Then, k independent hash functions, h 1 , h 2 , . . ., h k , with range {1, . . ., m} are used. For each element e i ∈ S, the bits at positions h 1 (e 1 ), h 2 (e 1 ), . . ., h k (e 1 ) in v are set to 1. Given a query for e j , the bits at positions h 1 (e j ), h 2 (e j ), . . ., h k (e j ) are checked. If any of them is 0, certainly e j is not in the set S. Otherwise, e j is accepted as a member of set S, although there is a probability that it is not a member [START_REF] Fan | Summary Cache: A Scalable Wide-area Web Cache Sharing Protocol[END_REF]. Independent of the size of the elements, less than 10 bits per element are required for a 1% false positive probability [START_REF] Bonomi | An Improved Construction for Counting Bloom Filters[END_REF].

We propose to use b bits per each element and k hash functions to minimize the false positive rate [START_REF] Fan | Summary Cache: A Scalable Wide-area Web Cache Sharing Protocol[END_REF]. We propose a custom SPARQL function CheckBloom(?commonAttribute, ?bitVector) which returns true if the positions corresponding to h 1 (?commonAttribute), h 2 (?commonAttribute), . . ., h k (?commonAttribute) are set to 1 in bloom filter ?bitVector. We explain the advantage of using a bloom filter in bind join by using the federated query example in Listing 1. Initially, the first subquery is executed on :service1 and then the second subquery is executed on :service2 with the bindings of the first subquery as shown in Listing 2. The intermediate results from :service1 can be seen from Table 1. Query size is proportional to the number of intermediate results, and the communication cost increases as the number of intermediate results increases. In order to decrease this cost, bind join can be employed by using a bloom filter as shown in Listing 3. BloomFilter is a bit array whose length in bits is equal to multiplication of the number of distinct common attribute values and b bits. Since our proposal uses b bits per each intermediate result, the size of the bloom filter in bits is equal to multiplication of the number of distinct common attribute values and b bits. On the other hand, bind join can be more efficient than bind-bloom join in some cases according to the number of false positives and the size of the result set. For this reason, our proposal estimates the remaining times of bind join and bind-bloom join when the tuples of a relation all arrive. Extended adaptive join operator for single join queries is depicted in Algorithm 1. Firstly, we send count queries to the endpoints of datasets R1 and R2 in order to learn their cardinalities. We always begin with symmetric hash join in order to minimize the response time. During the execution, when all the tuples from one dataset arrive and the tuples from the other dataset continue to arrive, we estimate the remaining times of continuing with symmetric hash join, switching to bind join, and switching to bind-bloom join. We decide the join method according to these cost estimations. If we switch to bind join or bind-bloom join, we emit the duplicate results of symmetric hash join with bind join or bind-bloom join. The cardinality estimation formula and the remaining time estimation formulas are presented in the following subsections.

Equation 3 shows the cost function of bind join where R i and R j are relations, |R| is the number of tuples in R, c t R is the transfer cost of R for each result tuple, and R j is the relation with the bindings of R i . In order to estimate the remaining times of bind join and bind-bloom join, we need the estimated cardinality of the second relation which is reduced by the bindings of the first relation, namely R j :

cost R i ( ⋈ BJ j i t i t j t R R c R c R c Ri Rj Rj ) = ⋅ + ⋅ + ⋅
(3) Algorithm 1. Extended adaptive join operator for single join queries Equation 4 depicts the cardinality estimation formula where |R i ⋈ R j_arrived | is the cardinality of R i ⋈ R j_arrived , |R j | is the cardinality of R j , |R j_arrived | is the cardinality of arrived tuples of R j , and ADF (R i , R j ) is the average duplication factor of R i on each common attribute value of R i and R j . The formula for ADF (R i , R j ) is depicted in Equation 5where |R i | is the cardinality of R i and |R i_uca | is the is the cardinality of unique common attribute values in R i . We use Equation 4 in order to calculate the estimated cardinality of R j when all the tuples of R i arrive. We expect that there is a directional proportion between the join cardinality and the number of tuples of R j :

R R R R R ADF R R j estimation i j arrived j j arrived i j _ _ _ ' . , = ( ) ⊳⊲ (4) ADF R R R R i j i i uca , _ ( ) = (5)
As stated earlier, when all the tuples of R i arrive, the algorithm estimates the remaining time if extended adaptive join operator continues with symmetric hash join, the remaining time if it changes the join method to bind join, and the remaining time if it changes the join method to bind-bloom join.

We have an idea about the data arrival rate of R j during the execution, so the estimation is possible. Equation 6shows the estimated remaining time, ERT SHJ , if extended adaptive join operator continues with symmetric hash join where |R j | is the cardinality of R j , |R j_arrived | is the cardinality of arrived tuples of R j , and t Rj_arrived is the time for R j_arrived tuples to arrive:

ERT R R t R SHJ j j arrived R j arrived j arrived = - ( ) ⋅ (6)
Equation 7 shows the estimated remaining time, ERT BJ , if the algorithm switches to bind join. |R i_uca | is the is the cardinality of unique common attribute values in R i , t ST is the time for sending one result tuple to the SPARQL endpoint of R j (≈ t Rj_arrived / |R j_arrived |), and |R j_estimation | is the estimated cardinality of R j which is reduced by the bindings of R i . |R j_arrived | is the cardinality of arrived tuples of R j , and t Rj_arrived is the time for R j_arrived tuples to arrive. The estimated remaining time for bind join includes sending all tuples of R i_uca to the endpoint of R j , and the retrieving time of R j from the endpoint of R j :

ERT R t R t R BJ i uca ST j estimation R j arrived j arrived = ⋅ ( ) + ⋅ _ _ _ ' _ (7)
Equation 8 shows the estimated remaining time, ERT BBJ , if the algorithm switches to bindbloom join where b is the number of bits per each element, |R i_uca | is the cardinality of unique common attribute values in R i , dr j is the data arrival rate (in bits/seconds) of the SPARQL endpoint (≈ s(|R j_arrived |) / |R j_arrived |, where s(|R j_arrived | is the size of R j_arrived tuples in bits), |R j_estimation | is the estimated cardinality of R j reduced by the bindings of R i , |fp| is the estimated cardinality of false positives, |R j_arrived | is the cardinality of arrived tuples of R j , and t Rj_arrived is the time for R j_arrived tuples to arrive. The estimated remaining time for bind-bloom join includes sending unique common tuples of R i in a bloom filter to the endpoint of R j , and the retrieving time of R j from the endpoint of R j :

ERT b R dr R fp t R BBJ i uca j j estimation R j arriv j arrived = ⋅ + + ( ) ⋅ _ _ _ ' _ e ed (8)
In multi-join queries, we begin with multi-way symmetric hash join [START_REF] Viglas | Maximizing the Output Rate of Multi-way Join Queries over Streaming Information Sources[END_REF] in order to minimize the response time as in single join queries. The algorithm for multijoin queries is depicted in Algorithm 2. When the tuples from a relation all arrive, called R i , the algorithm estimates the remaining times if the extended join operator switches to bind join or bind-bloom join for each relation which has a common attribute with R i . The algorithm chooses the relation with the minimum estimated bind join cost and the minimum estimated bind-bloom cost, called R j . It compares the estimated remaining times if it changes the join method to bind join or bind-bloom join for R i ⋈ R j with the estimated remaining time if the operator continues with multi-way symmetric hash join for all relations. The above procedure is repeated every time a relation is completely received.

We use the same formula, Equation 4, for single join queries and multi-join queries to estimate the cardinality of the second relation reduced by the bindings of the first relation. We need this estimation in order to calculate the estimated remaining time if extended adaptive join operator switches to bind join or bind-bloom join. Equation 9shows the estimated remaining time if the operator continues with multi-way symmetric hash join. Completion time is equal to the maximum completion time of the relations which compose the query:

ERT R R t R MSHJ k k arrived R k arrived k arrived = - ( ) ⋅         max | | _ _ _             ∈ ( )
where k n 1 2 , ,..,

Equation 10 shows the estimated remaining time if extended adaptive join operator uses bind join for R i and R j , and uses multi-way symmetric hash join for the other relations which are involved in the query. The estimated time if the operator uses bind join for R i and R j is depicted in Equation 11. |R i_uca | is the cardinality of unique common attribute values in R i , t ST is the time for sending one result tuple to the SPARQL endpoint of R j (≈_t Rj_arrived / |R j_arrived |), |R j_estimation | is the estimated cardinality of R j which is reduced by the bindings of R i , |R j_arrived | is the cardinality of arrived tuples of R j , t Rj_arrived is the time for R j_arrived tuples to arrive. ERT rest is the estimated remaining time for the rest of other relations to arrive and it is calculated by using Equation 12:

ERT ET ERT BJ R BJ R rest ij ij _ _ max ; = ( ) (10) ET R t R t R BJ R i uca ST j estimation R j arrived ij j arrived _ _ _ _ ' _ = ⋅ ( ) + ⋅ (11) ERT R R t R rest k k arrived R k arrived k arrived = - ( ) ⋅         max | | _ _ _             ∈ ( ) ≠ ≠ where k n and k i k j 1 2 , ,.., , (12)
Algorithm 2. Extended adaptive join operator for multi-join queries Equation 13shows the estimated remaining time if the extended adaptive join operator switches to bind-bloom join for R i and R j , and uses multi-way symmetric hash join for the other relations which are involved in the query. The estimated time if the operator uses bind-bloom join for R i and R j is depicted in Equation 14. b is the number of bits per each element, |R i_uca | is the cardinality of R i , and dr j is the data arrival rate (in bits/seconds) of the SPARQL endpoint (≈ s(|R j_arrived |) / |R j_arrived |, where s(|R j_arrived | is the size of R j_arrived tuples in bits). |R j_estimation | is the estimated cardinality of R j reduced by the bindings of R i , |fp| is the estimated cardinality of false positives, |R j_arrived | is the cardinality of arrived tuples of R j , and t Rj_arrived is the time for R j_arrived tuples to arrive. We use Equation 4and Equation 12 in order to calculate |R j_estimation | and ERT rest , respectively:

ERT ET ERT BBJ R BBJ R rest ij ij _ _ max ; = ( ) (13) ET b R dr R fp t R BBJ R i uca j j estimation R j ar ij j arrived _ _ _ _ ' _ = ⋅ + + ( ) ⋅ r rived (14)
In this section, first we explain the experimental environment, and then present evaluation on the performances of symmetric hash join/multi-way symmetric hash join, bind join, bind-bloom join, adaptive join operator and extended adaptive join operator for single join queries and multi-join queries. The focus of the evaluation is on their performances with respect to the response time and the completion time. Speedup 1 comparison between our previous proposal, adaptive join operator [START_REF] Oguz | Adaptive Join Operator for Federated Queries over Linked Data Endpoints[END_REF], and extended adaptive join operator is also presented to be self-contained and to show the contribution of our new proposal. Query cost in distributed environments is mainly dominated by the communication cost [START_REF] Ozsu | Principles of Distributed Database Systems[END_REF]. We conducted our experiments in the network simulator ns-3 2 to simulate the real network conditions and consider mainly the communication cost. We assume that the size of all queries is the same and each result tuple is considered to have the same size as well. Each query size is accepted as 500 bytes, whereas each result tuple size is employed as 250 bytes. Each count query size is assumed as 750 bytes and the message size is set to 100 tuples. Each selectivity factor is 0.5 / max(cardinality of R1, cardinality of R2) [START_REF] Shekita | Multi-Join Optimization for Symmetric Multiprocessors[END_REF]. We set the low, medium and high cardinality as 1000 tuples, 5000 tuples and 10000 tuples, respectively. Average duplication factors on the common attributes of relations are assigned randomly between 1 and 5, both inclusive. Average duplication factor = 1 means that there are not any duplicates, while average duplication factor = 5 means that there are 5 duplicates per value in average on the common attributes of the relations. For this reason, we ran each test 100 times when we assigned the duplication factors randomly. In some cases, we fixed the average duplication factors in order to understand the impact of the duplication factors as well. We used 8 bits per each element and 6 hash functions for bloom join with bloom filter. We conducted the simulations with different data arrival rates as explained in the following sections, however we always fixed their delays to 10 ms.

In this subsection, we compare extended adaptive join operator (EAJO) with symmetric hash join (SHJ), bind join (BJ), bind-bloom join (BBJ) and adaptive join operator (AJO) in two cases. We aim to show the impact of data sizes in the first case, whereas we focus on the effect of different data arrival rates in the second case. In addition, we compare AJO and EAJO with different m / n values and k independent hash functions where m refers to the number of bits in the bit vector, and n refers to the number of elements in the set.

The behaviours of the SHJ, BJ, BBJ, AJO and EAJO were analyzed when the data arrival rates of both endpoints were fixed to 0.5 Mbps while the data sizes of R1 and R2 were changed. In order to analyze all conditions, we evaluated the response time and the completion time when the data sizes of R1 and R2 were low-low (LL); low-medium (LM); low-high (LH); medium-low (ML); mediummedium (MM); medium-high (MH); high-low (HL); high-medium (HM) and high-high (HH), respectively. Average duplication factors on the common attributes of relations were given randomly between 1 and 5, both inclusive.

As Figure 1.a shows, BBJ and BJ have the worst response time in all conditions, whereas SHJ, AJO and EAJO behave similarly. As the data size of R1 increases, the response times of BJ and BBJ increase as well, due to waiting for the arrival of all results of R1 and sending the unique common attributes to the endpoint of R2. BBJ provides a slightly better response time than BJ due to the usage of bloom filter for sending the common attributes. On the other hand, SHJ, AJO and EAJO can generate the first result tuple as soon as there is a match between R1 and R2, without waiting for all tuples of R1 to arrive.

As shown in Figure 1.b, the completion time of BBJ is always shorter than BJ's due to the bloom filter usage. For this reason, we consider the completion times of BBJ instead of BJ's for comparing with others. When the cardinalities are low-medium, low-high and medium-high, (i.e., |R1| < |R2|), BBJ's completion time is the shortest. However, EAJO's completion time is quite similar to BBJ's because it changes the join method to BBJ when it decides that it is more efficient than SHJ or BJ. EAJO performs the best when the cardinalities of relations are medium-low, high-low and highmedium (i.e., |R1| > |R2|), respectively. When the cardinalities of R1 and R2 are the same, SHJ, AJO and EAJO provide the best performance in completion time at the same time. The data arrival rates and the cardinalities of the relations are the same in these cases. As a result, all the tuples of both relations arrive at the same time. SHJ is the most efficient join method for these cases. Therefore, both AJO and EAJO decide to continue with SHJ in such cases. To conclude the comparison of completion times, we can say that EAJO has the capability to choose the most efficient join method during the execution. For this reason, it provides or shares the best completion time in six of nine conditions. Also, it provides similar completion time to the best join method in the remaining three conditions.

Figure 1.c shows the speedup in completion time by EAJO compared to AJO. As shown in the figure, when the cardinalities of relations are different, EAJO provides speedup between 17.8% and 19.4%. The reason of the difference between the speedup percentages is based on the different average duplication factors. We can say the speedup of EAJO compared to AJO is 18.2% in average. EAJO does not provide speedup when the cardinalities of relations are the same, because both AJO and EAJO decide to continue with SHJ for the reasons explained previously.

In this case, we fixed the data arrival rate of R1 and changed the data arrival rate of R2. We conducted the simulations for two different cardinality options: i) low cardinality of R1 and high cardinality of R2; ii) high cardinality of R1 and low cardinality of R2. Average duplication factors on the common attributes of relations were given randomly between 1 and 5, both inclusive. However, we fixed the average duplication factors when we calculated the speedup of EAJO compared to AJO in order to understand the impact of the duplication factors as well.

We conducted the simulations for two different conditions: i) when the data arrival rate of R1 was fixed to 2 Mbps, and ii) when the data arrival rate of R1 was fixed to 0.5 Mbps. As Figures 2.a and 2.b show, the response times of BJ and BBJ are always longer than SHJ, AJO and EAJO. The gap between the response times of BJ and BBJ; and the others increases when the data arrival rate of R2 gets slower. SHJ provides the shortest response time in both conditions. AJO and EAJO provide almost the same response time due to beginning with SHJ. That is to say, SHJ, AJO and EAJO are the best in terms of response time at the same time.

As shown in Figure 2.c, the completion time of BBJ is always shorter than BJ due to the bloom filter usage. For this reason, we use the completion time of BBJ instead of the completion time of BJ when we compare the completion times of operators. BBJ provides the shortest completion time for all conditions because the first relation's cardinality is low and its data arrival rate is relatively fast. As the data arrival rate of the second relation gets faster, EAJO provides similar completion time with BBJ. The completion time of EAJO is always faster than SHJ and AJO. Figure 2.d shows the completion time comparison when the first relation's data arrival rate is fixed to 0.5 Mbps. BBJ provides the shortest completion time until the second relation's data arrival rate is 4.5 Mbps. However, EAJO has almost the same completion time with BBJ due to its ability to change the join method to BBJ during the execution. When the second relation's data arrival rate is faster or equal to 5.5 Mbps, SHJ provides the shortest completion time. In these cases, AJO and EAJO have the same completion time due to continuing with SHJ. That is to say, the winner of completion time is changed according to the data arrival rates. However, EAJO can choose the best join method during the execution.

Table 2 shows the speedup in completion time of EAJO compared to AJO when the data arrival rate of R1 is fixed to 2 Mbps and the data arrival rate of R2 is changed. The used average duplication factors are 1, 2 and 5, respectively where 1 means there are not any duplicates. For each data arrival rate of R2, AJO and EAJO change the join method to BJ and BBJ, respectively. Although EAJO provides speedup in all cases due to decreasing the data size of unique common attributes by using a bloom filter, the speedup decreases as the second relation's data arrival rate increases. The reason of this decrease in the speedup is because of the effect of the decrease in the size of the sent data as the network speed increases. Another key point to remember is that the speedup remains quite similar after a certain point due to the same reason. Table 3 3, the speedup decreases as the duplication factor increases.

We again conducted the simulations for two different conditions: i) when the data arrival rate of R1 was fixed to 2 Mbps, and ii) when the data arrival rate of R1 was fixed to 0.5 Mbps. The results observed from Figure 3 As shown in Figure 3.c, the completion time of EAJO is the best in all conditions. SHJ, BJ and BBJ wait the arrival of all tuples related to the first relation whose cardinality is high. However, AJO and EAJO can change the join method and the join order when the second relation's tuples all arrive. Compared to AJO, EAJO has the advantage of changing the join method to BBJ. Figure 3.d shows the completion time comparison when the first relation's data arrival rate is fixed to 0.5 Mbps. The results are similar to the previous one. EAJO's completion time is the shortest once again. The gap between the others is even higher.

Table 4 and Table 5 show the gained speedup in completion time by EAJO compared to AJO. In all conditions, both AJO and EAJO change the join order as R2 ⋈ R1. The gained time of EAJO compared to AJO remains the same, because the unique common attributes are sent to the endpoint of R1 and its data arrival rate is fixed. However, overall time decreases up to a certain value as the data arrival rate of R2 increases. For this reason, the speedup increases up to that certain value for both conditions as the data arrival rate of R2 increases. The speedup also increases as the duplication factor decreases.

As explained in the previous sections, a bloom filter represents a set S = {e 1 , e 2 , e 3 , . . ., e n } of n elements in a vector v of m bits. Initially all the bits are set to 0. Then, k independent hash functions, h 1 , h 2 , . . ., h k , with range {1, 2, . . ., m} are used. In this part, we analyze the impact of m / n by changing it between 2 and 22. In each m/n value, we used the number of hash functions, k, which minimizes the false positive rate [START_REF] Fan | Summary Cache: A Scalable Wide-area Web Cache Sharing Protocol[END_REF]. The m/n and k combinations used in our experiments can be seen from Table 6. We fixed the data arrival rates of both endpoints to 2 Mbps and the cardinalities of relations to low and high, respectively. First, average duplication factors on the common attribute of relations were given randomly between 1 and 5, both inclusive. Second, the average duplication factors were set to 2.

Figure 4.a shows the achieved speedup in completion time by EAJO compared to AJO in different m/n values when the average duplication factors are random. The results observed from the experiment appears to suggest that the gained speedup is not affected by the m/n value when it is between 6 and 20, inclusively. The best performance is provided when the m/n is equal to 8. The simulation results demonstrated that SHJ provides the best response time performance in all conditions due to being a non-blocking join operator which produces the first result tuple as early as possible. Our previous and current proposals, AJO and EAJO respectively, provide almost the same response time with SHJ due to setting the join method as SHJ in the beginning. The response times of BJ and BBJ are dramatically longer because of waiting for all tuples of the first relation to arrive. On the other hand, BJ or BBJ can provide better completion times when the first relation's cardinality is low and the second relation's cardinality is high. However, our previous proposal AJO can change the join method to BJ, and our new proposal EAJO can change the join method to BJ or BBJ in this condition.

EAJO provides the best completion time when the first relation's cardinality is high and the second relation's cardinality is low. This conclusion is valid in all data arrival combinations that we have tested.

To conclude, SHJ is the most successful join method in response time. However, the best join method in completion time can differ according to the relations' cardinalities and their data arrival rates. In addition, the results showed that BBJ provides better completion times than BJ in all conditions. These results seem to suggest that using bloom filters in bind join is a necessity. Our proposal, EAJO, provides an optimal response time by beginning with SHJ. It also provides an optimal completion time by changing the join method or join order during the execution. In brief, EAJO gives the best tradeoff between the response time and the completion time. Another key fact to remember is that EAJO always provides better completion time than AJO. In this subsection, we compare EAJO with multi-way symmetric hash join (MSHJ), BJ, BBJ, and AJO when there are three relations in the query. A query example that we use in our experiments is shown below. R1 (service1) and R2 (service2) have a common attribute, ?student, R2 and R3 (service3) have a common attribute, ?course.

Since our aim in this case is to show the impact of data sizes, we fixed the data arrival rates of all relations to 0.5 Mbps and the delays to 10 milliseconds. We conducted our experiments when the data sizes of R1, R2, R3 were low-low-low (LLL); low-medium-high (LMH); low-high-high (LHH); high-medium-low (HML); high-high-low (HHL); and high-high-high (HHH). As shown in Figures 5.a, 5.b and 5.c, in all cases, MSHJ, AJO and EAJO provide the best response time whereas BJ performs the worst response time and BBJ follows it. When the cardinality of R1 is high, the response times of BJ and BBJ become dramatically longer due to waiting for the arrival of all results of R1. As the duplication factor increases, the response times of BJ and BBJ shorten due to the decrease in the number of unique common attribute values. In other words, the number of attribute values to send to the other endpoints is decreased as the average duplication factor increases. Although the response times of BJ and BBJ decrease as the average duplication factor increases, their response times are dramatically longer than MSHJ, AJO and EAJO.

Figures 5.d, 5.e and 5.f show the completion times of MSHJ, BJ, BBJ, AJO and EAJO when the data arrival rates of all relations are fixed. When the cardinalities are HML or HHL, EAJO performs the best completion time and AJO has the closest completion time to it. The difference between EAJO and others, except AJO, is dramatically high. When the cardinalities of all relations are the same, namely LLL or HHH, MSHJ, AJO and EAJO share the best completion time whereas BJ performs the worst. When the cardinalities are LMH or LHH, BBJ performs the shortest completion time. EAJO's completion time is the second best when the average duplication factors are 1. BJ performs slightly better than EAJO when the average duplication factors are 2 or 5. To conclude, EAJO performs or shares the best completion time in four of six cases due to having the adaptation ability.

Table 7 shows the speedup in completion time of EAJO compared to AJO when the data arrival rates of R1, R2 and R3 are fixed. EAJO provides speedup from 6.40% to 31.33 when the cardinalities of relations are different. Although the speedup is not affected by the cardinalities of relations, it increases as the average duplication factors decrease. EAJO does not provide speedup when the cardinalities of relations are the same, because both AJO and EAJO decide to continue with MSHJ.

In order to show the impact of data arrival rates on MSHJ, BJ, BBJ, AJO and EAJO, we fixed the data arrival rates of R1 and R3 to 2 Mbps and changed the data arrival rate of R2. We conducted the simulations for two different cardinality options: i) low cardinality of R1, high cardinality of R2, and high cardinality of R3 (LHH); ii) high cardinality of R1, high cardinality of R2, and low cardinality of R3 (HHL). LHH and HHL are chosen because EAJO performs the worst and the best completion times among their results with other combinations in the previous section. Since we showed the effect of average duplication factors previously, we fixed the average duplication factors to 2 in these cases. Figure 6.a shows the response times of MSHJ, BJ, BBJ, AJO and EAJO when the cardinalities of relations are low, high and high respectively. As shown in the figure, response times of MSHJ, AJO and EAJO are almost the same whereas BJ's and BBJ's response times are highly slower. Figure 6.b indicates that the completion times in ascending order are of BBJ, BJ, EAJO, AJO and MSHJ. When the first relation's cardinality is low and its data arrival is relatively fast, BBJ and BJ provide better completion times. The completion time of MSHJ is the worst one in all cases due to having the disadvantage of waiting all the tuples of R2 and R3. However, AJO and EAJO change their join methods to BJ and BBJ, respectively, when the tuples of the first relation all arrive. Thus, EAJO performs almost the same completion time to BJ, and provides slightly worse completion time than BBJ. BBJ's and BJ's both response times and completion times would increase, if the first relation's cardinality were medium or high.

Figure 6.c shows the speedup in completion time of EAJO compared to AJO when the data arrival rate of R1 is fixed to 2 Mbps and the data arrival rate of R2 is changed with card(R1) << card(R2) = card(R3). As shown in the figure, the speedup decreases as the second relation's data arrival rate increases. The reason of this decrease in the speedup is because of the effect of the decrease in the size of the sent data as the network speed increases.

The results observed from Figure 7.a are similar to the results in Figure 6.a. BJ and BBJ have the worst response time again, whereas MSHJ, AJO and EAJO have almost the same response time. Since the cardinality of the first relation is high in this case, response times of BJ and BBJ are dramatically longer than others.

As shown in Figure 7.b, EAJO provides the best completion time in all cases. The completion times in ascending order are of EAJO, AJO, MSHJ, BBJ, and BJ when the second relation's data arrival rate is equal or faster than 1.5 Mbps. EAJO and AJO have the advantage of using BJ or BBJ when the tuples of R3 all arrive whose cardinality is low. EAJO outperforms AJO in all cases due to the usage of bloom filter for sending the common attributes. and R3 are low-high-high and high-high-low in these cases, respectively. The common attributes exist between R1 -R2; and R2 -R3. In the first case, when the cardinalities are low-high-high, first the tuples of R1 all arrive, and AJO and EAJO change the join method for R1 and R2 to BJ or BBJ, respectively. In the second case, when the cardinalities are high-high-low, first the tuples of R3 all arrive, and AJO and EAJO change the join method for R3 and R2 to BJ or BBJ, respectively. For this reason, the achieved speedups are the same in both cases.

The simulation results showed that MSHJ, which is a non-blocking join method, provides the best response time in all conditions. AJO and EAJO provide almost the same response time with MSHJ due to setting the join method as MSHJ at the beginning. The response times of BJ and BBJ are dramatically longer because of waiting the arrival of all tuples belonging to the first relation.

The results also demonstrated that BBJ provides the best completion time when the first relation's cardinality is low and the other relations' cardinalities are medium or high. However, EAJO can change the join method to BBJ in these conditions. On the other hand, EAJO provides the best completion time when the first relation's cardinality is high. This conclusion is valid in all data arrival combinations that we have tested.

In conclusion, MSHJ is the best join method in response time. However, the best join method in completion time differs according to the relations' cardinalities and data arrival rates. EAJO provides an optimal response time by beginning with MSHJ and an optimal completion time by changing the join method or join order during the execution. We can conclude that EAJO gives the best tradeoff between the response time and the completion time. We also emphasize that EAJO always provides better completion time than AJO.

Linked data contains two aspects: i) a way of publishing and connecting structured data on the web, and ii) the collection of interrelated data sources on the web. There are two main approaches to query these data sources which are link traversal [START_REF] Hartig | Executing SPARQL Queries over the Web of Linked Data[END_REF] and query federation (Görlitz & Staab, 2011a). Both approaches have the advantage of providing up-to-date results due to distributed query processing. However, link traversal has the weakness of not guaranteeing finding all results and has some performance problems. Because of these reasons, we turn our attention to the second approach.

Query federation is performed via an engine that distributes the query execution over a federation of SPARQL endpoints and has the following main steps: i) data source selection, ii) query optimization, and iii) query execution. Data source selection is responsible for selecting the relevant data sources for each triple pattern which composes the query. Query optimization groups the triple patterns, decides the join strategy and the join order. The last step is responsible for the execution of the query plan which is decided by the query optimizer.

The objective of the federated query engines can be stated as to minimize the response time and the completion time which include communication time, I/O time and CPU time. The communication time dominates the others in distributed environments. Since the subqueries and intermediate results are transmitted over the web of data, the communication cost is affected by the amount of intermediate results. It is substantially affected by the join order and the join method which are decided in the query optimization phase.

Static query optimization and heuristics are widely used in query federation [START_REF] Quilitz | Querying Distributed RDF Data Sources with SPARQL[END_REF][START_REF] Görlitz | SPLENDID: SPARQL Endpoint Federation Exploiting VOID Descriptions[END_REF][START_REF] Schwarte | FedX: Optimization Techniques for Federated Query Processing on Linked Data[END_REF][START_REF] Wang | LHD: Optimising Linked Data Query Processing Using Parallelisation[END_REF]. However, federated query processing is done on the distributed data sources on the web which causes unpredictable data arrival rates. In addition, most of the statistics are missing or unreliable. For these reasons, we think that adaptive query optimization [START_REF] Deshpande | Adaptive Query Processing[END_REF] is a need in this unpredictable environment. ANAPSID [START_REF] Acosta | ANAPSID: An Adaptive Query Processing Engine for SPARQL Endpoints[END_REF] and ADERIS [START_REF] Lynden | Adaptive Integration of Distributed Semantic Web Data[END_REF][START_REF] Lynden | ADERIS: An Adaptive Query Processor for Joining Federated SPARQL Endpoints[END_REF] are the two query federation engines which use adaptive query optimization. ANAPSID uses a non-blocking join method based on symmetric hash join [START_REF] Wilschut | Dataflow Query Execution in a Parallel Main-Memory Environment[END_REF] and Xjoin [START_REF] Urhan | XJoin: A Reactively-Scheduled Pipelined Join Operator[END_REF]. ADERIS [START_REF] Lynden | Adaptive Integration of Distributed Semantic Web Data[END_REF] joins two predicate tables as they become complete, whereas ADERIS [START_REF] Lynden | ADERIS: An Adaptive Query Processor for Joining Federated SPARQL Endpoints[END_REF]) employs a cost model for dynamically changing the join order. Also, AVALANCHE [START_REF] Basca | Avalanche: Putting the Spirit of the Web back into Semantic Web Querying[END_REF][START_REF] Basca | Querying a messy web of data with Avalanche[END_REF] considers adaptivity. It collects statistical information about relevant data sources and then generates its execution plan to provide the first k tuples. Our previous proposal [START_REF] Oguz | Adaptive Join Operator for Federated Queries over Linked Data Endpoints[END_REF], to the best of our knowledge, is the first study that considers an adaptive join operator that aims to reduce both the response time and the completion time when query execution is done over SPARQL endpoints. In this paper, we present the improved version of it which achieves to further minimize the completion time.

Table 8 shows the comparison of adaptive query optimization in query federation depending on the following criteria:

• Server (S): Indicates the type of the server for publication and querying of linked data. SPARQL Endpoints (se) and triple pattern fragment servers (tpfs) are the possible values; • Join Method (JM): Shows the used join methods in the studies which are categorized as nested loop join (nlj), index nested loop join (inlj), symmetric hash join (shj), bind join (bj), and bindbloom join (bbj); As shown in Table 8, ADERIS, ANAPSID, AVALANCHE, AJO and EAJO use adaptive query optimization for the queries over SPARQL endpoints, whereas nLDE employs adaptive query optimization for queries over triple pattern fragments. The proposals for the SPARQL endpoints prefer to collect the statistics in runtime due to unreliable or missing statistics. Therefore, up-to-dateness of statistics is provided. On the other hand, nLDE uses metadata catalogs for the statistics because triple pattern fragments contain both data, metadata and controls.

The second parameter in Table 8 is the join method. Bind join is used by all the studies, except nLDE, and nested loop join is employed by ADERIS and nLDE. ANAPSID proposes two join methods which are agjoin and adjoin. The first one is a non-blocking join method which is based on symmetric hash join and XJoin. The second one is the extended version of dependent join [START_REF] Florescu | Query Optimization in the Presence of Limited Access Patterns[END_REF] which sends the request to the second data source when tuples from the first source are received. Adjoin can be accepted as a bind join because it needs the bindings. As illustrated in Table 8, ANAPSID, AJO, nLDE and EAJO have the opportunity to produce results incrementally since they use symmetric hash join. AVALANCHE defines its join method as distributed join and it employs bloom filter optimised joins to reduce communication cost. The difference between distributed join and bind join is not explained in their papers. We categorize its join methods as bind join and bind-bloom join. In brief, AVALANCHE and EAJO can use bind-bloom join which has the advantage of decrease the completion time. The third parameter for the comparison is the frequency of feedback. The studies in inter-operator level collect feedback from different physical operators and react to the execution of them according to the feedback. On the other hand, feedback is collected during the processing of the physical operator in the intra-operator level. The limit of collection can vary from a single tuple to a block of tuples [START_REF] Gounaris | Adaptive Query Processing: A Survey[END_REF]. ADERIS and AVALANCHE have the inter-operator feedback frequency, whereas ANAPSID, nLDE, AJO and EAJO have the intra-operator one. ANAPSID's feedback belongs to using an adaptive operator. The difference between the intra-operator of nLDE and AJO/EAJO is based on the amount of accumulated data before reacting. Although nLDE checks the feedback for each tuple, AJO and EAJO do it when all tuples of a relation arrive. The next parameter is the type of event. ANAPSID, AVALANCHE, AJO and EAJO focus on data arrival rates, whereas ADERIS and nLDE check their decisions at each step.

AJO and EAJO distinguish from others when we consider the sixth and seventh parameters in Table 8, namely logical plan and physical plan. Different from others, AJO and EAJO provide reformulation of the remaining plan at the logical level, and operator replacement at the physical level by the ability of changing both the join order and the join method.

The last comparison parameter is the type of modification. ANAPSID's type of modification belongs to a dynamic operator, whereas the types of modification of ADERIS, AVALANCHE and nLDE are rescheduling due to changing the join order for the rest of the query. AJO and EAJO, besides rescheduling, cover replacement which has the meaning of changing the join method.

In this paper, we presented an adaptive join operator for single join queries and multi-join queries which is an extended version of our previous work [START_REF] Oguz | Adaptive Join Operator for Federated Queries over Linked Data Endpoints[END_REF]. We improved our previous adaptive join operator to further reduce the communication cost. For this reason, we integrated bindbloom join to our operator. Our new proposal always begins with symmetric hash join (multi-way symmetric hash join for multi-join queries) in order to provide optimal response time. It can change the join method to bind join or bind-bloom join when it decides that the candidate join method is more efficient than symmetric hash join for the rest of the query.

The results of the performance evaluation showed the efficiency of the proposed join operator. Compared to symmetric hash join and multi-way symmetric hash join, it provides faster completion times and almost the same response times. Compared to bind join and bind-bloom join, the extended operator performs substantially better with respect to the response time and it can also improve the completion time. Furthermore, the extended operator provides faster completion time than our previous operator in all conditions, because it uses a bloom filter for sending the common attributes to the other endpoint. Experimental results also showed that bind-bloom join provides better completion times than bind join in all conditions. These results allow us to suggest using bloom filters in bind join. This work is partially supported by The Scientific and Technological Research Council of Turkey (TUBITAK).

  .a and Figure 3.b are similar to the results in Figure 2.a and Figure 2.b. Since the cardinality of the first relation is high in this case, response times of BJ and BBJ are dramatically longer than SHJ and also longer than AJO and EAJO as expected. The response times of SHJ, AJO and EAJO are nearly the same.

Figure 4 .

 4 b shows the gained speedup in completion time by EAJO when the average duplication factors are set to 2. The results are similar to the results in Figure 4.a. Since the m/n is between 8 and 16, the speedup values are almost the same.

Figure 7 .

 7 Figure7.c shows the speedup in completion time of EAJO compared to AJO when the data arrival rate of R1 is fixed to 2 Mbps and the data arrival rate of R2 is changed with card(R1) = card(R2) >> card(R3). The speedup is gained due to the usage of bloom filter and hence sending less data size through the network. The speedup decreases as the second relation's data arrival rate increases, because the effect of the decrease in the size of the sent data decreases as the network speed increases. The results are the same with the results in Figure6.c. The cardinalities of R1, R2 and R3 are low-high-high and high-high-low in these cases, respectively. The common attributes exist between R1 -R2; and R2 -R3. In the first case, when the cardinalities are low-high-high, first the tuples of R1 all arrive, and AJO and EAJO change the join method for R1 and R2 to BJ or BBJ, respectively. In the second case, when the cardinalities are high-high-low, first the tuples of R3 all arrive, and AJO and EAJO change the join method for R3 and R2 to BJ or BBJ, respectively. For this reason, the achieved speedups are the same in both cases.

•

  Type of Statistics (ToS): States of the collection time of statistics which has the following values: runtime (rt) and metadata (md); • Frequency of Feedback (FoF): Shows the level of modification and has two possible values: inter-operator (inter) and intra-operator (intra); • Type of Event (ToE): Shows the case triggering the decision and has two values which are data arrival rates (dar) and any; • Logical Plan (LP): Displays the query plan modifications at the logical level and are categorized as reformulation of the remaining plan (rf), operator reordering (op_ro), and no effects (no) for adaptive query optimization in relational databases by Gounaris et al. (Gounaris, Paton, Fernandes, & Sakellariou, 2002). Reformulation of the remaining plan includes the operator reordering; • Physical Plan (PP): Represents the query plan modifications at the physical level and are categorized as usage of adaptive operators (uao), operator replacement (op_rep), and no effects (no) for relational databases by Gounaris et al. (Gounaris et al., 2002); • Type of Modification (ToM): Can be employed as rescheduling (rs), dynamic operator (do), and rescheduling and replacement (rs & rp).

  shows the speedup gained by EAJO when the s data arrival rate is fixed to 0.5 Mbps. In this case, EAJO provides speedup until the second relation's data arrival rate is equal or faster than 4.5 Mbps, because both AJO and EAJO decide to continue with SHJ after this data arrival rate. As shown in both Table2 and Table

	first relation'
	Data Arrival Rate of R2		Average Duplication Factors
	in Mbps	1	2	3
	0.5	35.28%	22.53%	11.57%
	1.5	25.65%	13.99%	7.07%
	2.5	20.39%	10.71%	5.70%
	3.5	15.99%	8.47%	4.80%
	4.5	12.51%	7.44%	4.47%
	5.5	10.55%	6.81%	4.32%
	6.5	9.64%	6.37%	4.24%
	Data Arrival Rate of R2		Average Duplication Factors
	in Mbps	1	2	3
	0.5	30.61%	18.62%	9.16%
	1.5	17.29%	8.72%	4.20%
	2.5	12.41%	6.08%	3.12%
	3.5	9.75%	4.91%	2.71%
	4.5	-	4.27%	2.51%

Data Sizes ofR1, R2 and R3 Average Duplication Factors

		1	2	3
	LMH	31.33%	16.55%	6.40%
	LHH	31.33%	16.55%	6.40%
	HML	31.33%	16.55%	6.40%
	HHL	31.33%	16.55%	6.40%