HYPERTREE DECOMPOSITION FOR SOLVING CONSTRAINT SATISFACTION PROBLEMS

Abdelmalek Ait-Amokhtar, Kamal Amroun, Zineb Habbas

2009

Abstract

This paper deals with the structural decomposition methods and their use for solving Constraint Satisfaction problems (CSP). mong the numerous structural decomposition methods, hypertree decomposition has been shown to be the most general CSP decomposition. However so far the exact methods are not able to find optimal decomposition of realistic instances in a reasonable CPU time. We present Alea, a new heuristic to compute hypertree decomposition. Some experiments on a serial of benchmarks coming from the literature or the industry permit us to observe that Alea is in general better or comparable to BE (Bucket Elimination), the best well known heuristic, while it generally outperforms DBE (Dual Bucket Elimination), another successful heuristic. We also experiment an algorithm (acyclic solving algorithm) for solving an acyclic CSP obtained by using the heuristic Alea. The experimental results we obtain are promising comparing to those obtained by solving CSP using an enumerative search algorithm.

References

  1. C.Bessière, P. Meseguer, C. F. and Larossa, J. (2002). On forward checking for non binary constraint satisfaction. Artificial Intelligence, 141:205-224.
  2. Cohen, D., Jeavons, P., and Gyssens, M. (2005). A unified theory of structural tractability for constraint satisfaction problems and spread cut decomposition. In Proceedings of IJCAI 2005, pages 72-77.
  3. Dechter, R. (2003). Constraint Processing. Morgan Kaufmann.
  4. Dechter, R., Dechter, A., and Pearl, J. (1988). Optimization in constraint-networks. In Proceedings of the Conference on Influence Diagrams for Decision Analysis: Inference and prediction, Berkeley.
  5. Dechter, R. and Pearl, J. (1989). Tree clustering for constraint networks. Artificial Intelligence, 38:353-366.
  6. Dermaku, A., Ganzow, T., Gottlob, G., McMahan, B., Musliu, N., and Samer, M. (2005). Heuristic methods for hypertree decompositions. Technical report, DBAI-R.
  7. Freuder, E. C. (1982). A sufficient condition for backtrackfree search. Journal of the Association for Computing Machinery, 29:24-32.
  8. Ganzow, T., Gottlob, G .and Musliu, N., and Samer, M. (2005). A csp hypergraph library. Technical report, DBAI-TR-2005-50, Technische Universitt Wien.
  9. Gottlob, G., Grohe, M., and Musliu, N. (2005). Hypertree decomposition: structure, algorithms and applications. In Proceeding of 31 st International workshop WG, Metz.
  10. Gottlob, G., Leone, N., and Scarcello, F. (1999a). A comparison of structural csp decomposition methods. In Proceedings of IJCAI'99, pages 394-399.
  11. Gottlob, G., Leone, N., and Scarcello, F. (1999b). On tractable queries and constraints. In Proceedings of DEXA'99.
  12. Gottlob, G., Leone, N., and Scarcello, F. (2000). A comparison of structural csp decomposition methods. Artificial Intelligence, 124:243-282.
  13. Gottlob, G., Leone, N., and Scarcello, F. (2001). Hypertree decompositions: A survey. In Proceedings of MFCS 7801, pages 37-57.
  14. Gottlob, G. and Samer, M. (2007). A backtraching based algorithm for computing hypertree decompositions. arXivics.DS 0701083vl 14 Jan 2007.
  15. Gyssens, M., Jeavons, P. G., and Cohen, D. A. (1994). Decomposing constraint satisfaction problems using database techniques. Artificial Intelligence, 66:57-89.
  16. Harvey, P. and Ghose, A. (2003). Reducing redundancy in the hypertree decomposition scheme. In Proceding of ICTAI'03, pages 548-555, Montreal.
  17. Jeavons, P. G., A, C. D., and Gyssens, M. (1994). A structural decomposition for hypergraphs. Contemporary Mathematics, 178:161-177.
  18. Korimort, T. (April 2003). Heuristic decomposition Hypertree Decomposition. PhD thesis, Vienna University of Technology.
  19. McMahan, B. (2003). Bucket elimination and hypertree decompositions. Technical report, Implementation report, institute of information systems (DBAI), TU, Vienna.
  20. Montanari, U. (1974). Networks of constraints: Fundamental properties and applications to pictures processing. Information Sciences, 7:95-132.
  21. Musliu, N. and Schafhauser, W. (2007). Genetic algorithms for generalized hypertree decompositions. European Journal of Industrial Engineering, 1(3):317-340.
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Paper Citation


in Harvard Style

Ait-Amokhtar A., Amroun K. and Habbas Z. (2009). HYPERTREE DECOMPOSITION FOR SOLVING CONSTRAINT SATISFACTION PROBLEMS . In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-8111-66-1, pages 85-92. DOI: 10.5220/0001662400850092


in Bibtex Style

@conference{icaart09,
author={Abdelmalek Ait-Amokhtar and Kamal Amroun and Zineb Habbas},
title={HYPERTREE DECOMPOSITION FOR SOLVING CONSTRAINT SATISFACTION PROBLEMS},
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2009},
pages={85-92},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001662400850092},
isbn={978-989-8111-66-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - HYPERTREE DECOMPOSITION FOR SOLVING CONSTRAINT SATISFACTION PROBLEMS
SN - 978-989-8111-66-1
AU - Ait-Amokhtar A.
AU - Amroun K.
AU - Habbas Z.
PY - 2009
SP - 85
EP - 92
DO - 10.5220/0001662400850092


in Harvard Style

Ait-Amokhtar A., Amroun K. and Habbas Z. (2009). HYPERTREE DECOMPOSITION FOR SOLVING CONSTRAINT SATISFACTION PROBLEMS.In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-8111-66-1, pages 85-92. DOI: 10.5220/0001662400850092


in Bibtex Style

@conference{icaart09,
author={Abdelmalek Ait-Amokhtar and Kamal Amroun and Zineb Habbas},
title={HYPERTREE DECOMPOSITION FOR SOLVING CONSTRAINT SATISFACTION PROBLEMS},
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2009},
pages={85-92},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001662400850092},
isbn={978-989-8111-66-1},
}


in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - HYPERTREE DECOMPOSITION FOR SOLVING CONSTRAINT SATISFACTION PROBLEMS
SN - 978-989-8111-66-1
AU - Ait-Amokhtar A.
AU - Amroun K.
AU - Habbas Z.
PY - 2009
SP - 85
EP - 92
DO - 10.5220/0001662400850092