A Forward-Checking algorithm based on a Generalised Hypertree Decomposition for solving non-binary constraint satisfaction problems

Abstract

International audienceMethods exploiting hypertree decompositions are considered as the best approach for solving extensional constraint satisfaction problems (CSPs) on finite domains, with regard to theoretical time complexity when fixed widths are considered. However, this result has not been confirmed in practice because of the memory explosion problem. In this article, a new approach for efficient solving extensional non-binary CSPs is proposed. It is a combination of an enumerative search algorithm which is memory efficient and a Generalised Hypertree Decomposition (GHD) that is time efficient. This new approach is a cluster-oriented Forward-Checking algorithm. It considers the solutions of the subproblems deriving from the decomposition, as the values to be assigned rather than the values associated with the variables of the initial problem. In addition, the algorithm is guided by an order induced by the clusters deriving from the GHD. Moreover, two improved versions of this algorithm are proposed. The first version uses nogoods and the second one improves it again by a dynamic reordering of subtrees. All these algorithms have been implemented and the experimental results are promising

Hypertree Decompositions

“…Constraint satisfiability is feasible in polynomial time on classes of instances having bounded hypertree width [74]. The result is the natural consequence of the fact that constraint satisfiability is essentially the same problem of answering conjunctive queries, reformulated in a different context and with a different syntax (see, e.g., [10,93] for a recent implementation in the CSP area). Indeed, as said in Section 1.7, the two settings (CSPs and conjunctive queries) can be abstractly viewed as special instances of the homomorphism problem, which takes as input two finite relational structures A and B, and asks whether there is a homomorphism from A to B [108].…”

HyperBench: A Benchmark and Tool for Hypergraphs and Empirical Findings

“…For the analysis of CSPs, much less work has been done. Although it has been shown that exploiting (hyper-)tree decompositions may significantly improve the performance of CSP solving [4,33,35,39], a systematic study on the (generalized) hypertree width of CSP instances has only been carried out by few works [30,39,51]. To the best of our knowledge, we are the first to analyze the hw, ghw, and fhw of ca.…”

“…Hypergraph decompositions have meanwhile found their way into commercial database systems such as LogicBlox [5,8,36,37,46] and advanced research prototypes such as EmptyHeaded [1,2,47,55]. Hypergraph decompositions have also been successfully used in the CSP area [4,33,39]. In theory, the pros and cons of various notions of decompositions and widths are well understood (see [24] for a survey).…”

Fast and parallel decomposition of constraint satisfaction problems

“…In fact, in [1] a speed-up up to a factor of 2,500 was reported for the CQs studied there. Structural decompositions are therefore already being used in commercial products and research prototypes, both in the CSP area as well as in database systems [1,4,5,27,33]. However, previous decomposition algorithms are limited in that they fail to find optimal decompositions (i.e., decompositions of minimal width) even for low widths.…”