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...is of our data structures and algorithm; and, d) An empirical evaluation of PerFB comparing its performance to that of PerTuple. In addition to the contribution of Samaras & Stergiou [22], our approach is related to the following research. Karakashian et al. propose a compact data structure, the index tree, which finds coarse blocks and stores them in the leaves of the tree [16]. However, they fall short of exploiting them to improve constraint propagation. Lecoutre et al. propose the algorithm STR3 to enforce GAC using the size of the blocks induced, on a relation, by a variable in its scope [19]. Further, Lecoutre et al. propose the algorithm eSTR to enforce pairwise-consistency using only the size of the coarse blocks [20]. Our work is also related to the computation of subproblem interchangeability [4, 5, 7, 18], where the variables’ domains (instead of constraints’ relations) are dynamically partitioned by the constraints of a specified subproblem. This paper is organized as follows. Section 2 gives some background information. Section 3 discusses relation partitioning. Section 4 describes how to create relation partitions and the data structures for storing them. Section 5 gives ...

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...). Indeed, they are often required when modeling combinatorial problems in many application fields. The design of filtering algorithms for such constraints has generated a lot of research effort, see =-=[2, 19, 16, 8, 27, 14, 15, 21, 24]-=-. The biggest problem with table constraints are their size. Several approaches have been proposed to reduce this size. Two of them modify the definition of classical tuples: compressed tuples [12, 25...

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...rt, leaving the relations unchanged. Simple Tabular Reduction (STR) algorithms not only enforce GAC on the domains, but also remove all tuples τ ∈ Rj where ∃xi ∈ scope(Rj) such that τ [xi] /∈ dom(xi) =-=[21, 13, 14]-=-. A CSP is m-wise consistent if, every tuple in a relation can be extended to every combination of m−1 other relations in a consistent manner [8, 10]. Keeping with relational-consistency notations, Ka...

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... arbitrary constraints that run in time O(nd) (where n is the number of variables and d is the maximum domain size), in extreme cases an exponential factor faster than any table constraint propagator =-=[3, 7, 9, 5, 6, 10, 11, 12, 13]-=-. As our experiments show, generated propagators can even outperform hand-optimised propagators when performing the same propagation. It can take substantial time to generate a GAC propagator, however...