Bi-Objective Optimization Method for Horizontal Fragmentation Problem in Relational Data Warehouses as a Linear Programming Problem

In this work, we relied on a particular exact method to solve NP-Hard problem of determining a horizontal fragmentation scheme in relational data warehouses. The method used is that of linear programming which is distinguished by other methods by the existence of practical methods that facilitate the resolution of problems that may be described in linear form. We quote the Simplex method and the interior points. To meet the linearity of the objective function and constraints, we used initially “De Morgan” theorem, which is based on properties of sets to transform and optimize decision queries, from any form to a linear one.

In addition to designing and solving the selection problem of horizontal fragmentation technique, we considered the problem in two simultaneous objectives, namely: the number of Inputs/Outputs needed to run the global workload, and number of fragments generated to identify the best solutions compared to the concept of Pareto dominance.

In addition, to carry out our work, we used the Benchmark APB1 invoked by a workload, to achieve satisfactory results.