Generalized Hypertree Decomposition for solving non binary CSP with compressed table constraints

Habbas, Zineb; Amroun, Kamal; Singer, Daniel

RAIRO - Operations Research - Recherche Opérationnelle, Special issue: Research on Optimization and Graph Theory dedicated to COSI 2013 / Special issue: Recent Advances in Operations Research in Computational Biology, Bioinformatics and Medicine, Tome 50 (2016) no. 2, pp. 241-267.

Many real-world problems can be modelled as Constraint Satisfaction Problems (CSPs). Although CSP is NP-complete, it has been proved that non binary CSP instances may be efficiently solved if they are representable as Generalized Hypertree Decomposition (GHD) with small width. Algorithms for solving CSPs based on a GHD consider an extensional representation of constraints together with join and semi-join operations giving rise to new large constraint tables (or relations) needed to be temporarily saved. Extensional representation of constraints is quite natural and adapted to the specification of real problems but unfortunately limits significantly the practical performance of these algorithms. The present work tackles this problem using a compact representation of constraint tables. Consequently, to make algorithms compatible with this compact representation, new “compressed join” and “compressed semi-join” operations have to be defined. This last step constitutes our main contribution which, as far as we know, has never been presented. The correctness of this approach is proved and validated on multiple benchmarks. Experimental results show that using compressed relations and compressed operations improves significantly the practical performance of the basic algorithm proposed by Gottlob et al. for solving non binary CSPs with a Generalized Hypertree Decomposition.

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