article

Hybrid backtracking bounded by tree-decomposition of constraint networks

Authors:

Philippe Jégou,

Cyril TerriouxAuthors Info & Claims

Artificial Intelligence, Volume 146, Issue 1

Pages 43 - 75

https://doi.org/10.1016/S0004-3702(02)00400-9

Published: 01 May 2003 Publication History

Abstract

We propose a framework for solving CSPs based both on backtracking techniques and on the notion of tree-decomposition of the constraint networks. This mixed approach permits us to define a new framework for the enumeration, which we expect that it will benefit from the advantages of two approaches: a practical efficiency of enumerative algorithms and a warranty of a limited time complexity by an approximation of the tree-width of the constraint networks. Finally, experimental results allow us to show the advantages of this approach.

References

[1]

{1} S. Arnborg, D. Corneil, A. Proskuroswki, Complexity of finding embedding in a k-tree, SIAM J. Discrete Math. 8 (1987) 277-284.]]

Digital Library

[2]

{2} A. Berry, A wide-range efficient algorithm for minimal triangulation, in: Proceedings of SODA'99 SIAM Conference, 1999.]]

[3]

{3} A. Becker, D. Geiger, A sufficiently fast algorithm for finding close to optimal clique trees, Artificial Intelligence 125 (2001) 3-17.]]

Digital Library

[4]

{4} R.J. Bayardo, D.P. Miranker, An optimal backtrack algorithm for tree-structured constraint satisfaction problems, Artificial Intelligence 71 (1994) 159-181.]]

Digital Library

[5]

{5} R.J. Bayardo, D.P. Miranker, A complexity analysis of space-bounded learning algorithms for the constraints satisfaction problem, in: Proceedings of 13th National Conference on Artificial Intelligence, Portland, OR, 1996, pp. 298-304.]]

[6]

{6} R. Bayardo, J. Pehoushek, Counting models using Connected Components, in: Proceedings of AAAI 2000, Austin, TX, 2000, pp. 157-162.]]

[7]

{7} C. Bessière, J. -C. Régin, MAC and combined heuristics: Two reasons to forsake FC (and CBJ?) on hard problems, in: Proceedings of CP'96, 1996, pp. 61-75.]]

Digital Library

[8]

{8} C. Bessière, J. -C, Régin, Refining the basic constraint propagation algorithm, in: Proceedings of the 17th International Joint Conference on Artificial Intelligence, Seattle, WA, 2001, pp. 309-315.]]

Digital Library

[9]

{9} J. -F. Baget, Y. Tognetti, Backtracking through biconnected components of a constraint graph, in: Proceedings of the 17th International Joint Conference on Artificial Intelligence, Seattle, WA, 2001, pp. 291-296.]]

Digital Library

[10]

{10} C. Cabon, S. de Givry, L. Lobjois, T. Schiex, J.P. Warners, Radio link frequency assignment, Constraints 4 (1999) 79-89.]]

[11]

{11} X. Chen, P. van Beek, Conflict-directed backjumping revisited, J. Artificial Intelligence Res. 14 (2001) 53-81.]]

Digital Library

[12]

{12} R. Dechter, Enhancement schemes for constraint processing: Backjumping, learning, and cutset decomposition, Artificial Intelligence 41 (1990) 273-312.]]

Digital Library

[13]

{13} R. Dechter, Y. El Fattah, Topological parameters for time-space tradeoff, Artificial Intelligence 125 (2001) 93-118.]]

Digital Library

[14]

{14} R. Dechter, J. Pearl, The cycle-cutset method for improving search performance in AI applications, in: Proceedings of the Third IEEE on Artificial Intelligence Applications, 1987, pp. 224-230.]]

[15]

{15} R. Dechter, J. Pearl, Tree-clustering for constraint networks, Artificial Intelligence 38 (1989) 353-366.]]

Digital Library

[16]

{16} E. Freuder, A sufficient condition for backtrack-free search, J. ACM 29 (1982) 24-32.]]

Digital Library

[17]

{17} J. Gaschnig, Performance Measurement and Analysis of Certain Search Algorithms, Technical Report CMU-CS-79-124, Carnegie-Mellon University, 1979.]]

[18]

{18} M. Ginsberg, Dynamic backtracking, J. Artificial Intelligence Res. 1 (1993) 25-46.]]

Digital Library

[19]

{19} G. Gottlob, N. Leone, F. Scarcello, A comparison of structural CSP decomposition methods, Artificial Intelligence 124 (2000) 282-343.]]

Digital Library

[20]

{20} M. Golumbic, Algorithmic Graph Theory aad Perfect Graphs, Academic Press, New York, 1980.]]

[21]

{21} R. Haralick, G. Elliot, Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence 14 (1980) 263-313.]]

[22]

{22} A. Koster, Frequency assignment--models and algorithms, PhD Thesis, University of Maastricht, November 1999.]]

[23]

{23} G. Kondrak, P. van Beek, A theorical evaluation of selected backtracking algorithms, Artificial Intelligence 89 (1997) 365-387.]]

Digital Library

[24]

{24} J. Larrosa, Boosting search with variable elimination, in: Proceedings of the 6th CP, 2000.]]

[25]

{25} A. Mackworth, Consistency in networks of relations, Artificial Intelligence 8 (1977) 99-118.]]

Digital Library

[26]

{26} U. Montanari, Networks of constraints: Fundamental properties and applications to picture processing, Artificial Intelligence 7 (1974) 95-132.]]

[27]

{27} B. Nadel, Tree search and arc consistency in constraint-satisfaction algorithms, in: Search in Artificial Intelligence, Springer, Berlin, 1988, pp. 287-342.]]

[28]

{28} P. Prosser, Hybrid algorithms for the constraint satisfaction problem, Comput. Intelligence 9 (1993) 268-299.]]

[29]

{29} N. Robertson, P.D. Seymour, Graph minors II: Algorithmic aspects of tree-width, Algorithms 7 (1986) 309-322.]]

[30]

{30} D. Rose, R. Tarjan, G. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput. 5 (1976) 266-283.]]

[31]

{31} D. Sabin, E. Freuder, Contradicting conventional wisdom in constraint satisfaction, in: Proceedings of 11th ECAI, 1994, pp. 125-129.]]

[32]

{32} T. Schiex, H. Fargier, G. Verfaillie, Valued constraint satisfaction problems: Hard and easy problems, in: Proceedings of the 14th International Joint Conference on Artificial Intelligence, Montreal, Quebec, 1995, pp, 631-637.]]

[33]

{33} R. Stallman, G. Sussman, Forward reasoning and dependency-directed backtracking in a system for computer-aided circuit analysis, Artificial Intelligence 9 (1977) 135-196.]]

[34]

{34} T. Schiex, G. Verfaillie, Nogood recording for static and dynamic constraint satisfaction problems, Internat. J. Artificial Intelligence Tools 3 (2) (1994) 187-207.]]

[35]

{35} R. Tarjan, M. Yannakakis, Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs, SIAM J. Comput. 13 (3) (1984) 566-579.]]

Digital Library

[36]

{36} G. Verfaillie, M. Lemaître, T. Schiex, Russian doll search for solving constraint optimization problems, in: Proceedings of the 13th AAAI, Portland, OR, 1996, pp. 181-187.]]

Cited By

Irfan MChan HSoundy JKiyavash NMooij J(2024)Equilibrium computation in multidimensional congestion gamesProceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence10.5555/3702676.3702758(1751-1779)Online publication date: 15-Jul-2024
https://dl.acm.org/doi/10.5555/3702676.3702758
Petrova ALarrosa J(2023)On Learning When to Decompose Graphical ModelsLearning and Intelligent Optimization10.1007/978-3-031-44505-7_19(270-285)Online publication date: 4-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-44505-7_19
Peruvemba Ramaswamy VSzeider S(2020)MaxSAT-Based Postprocessing for TreedepthPrinciples and Practice of Constraint Programming10.1007/978-3-030-58475-7_28(478-495)Online publication date: 7-Sep-2020
https://dl.acm.org/doi/10.1007/978-3-030-58475-7_28
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Index Terms

Hybrid backtracking bounded by tree-decomposition of constraint networks
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms
    1. Algorithm design techniques
      1. Backtracking
  2. Models of computation
    1. Computability

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Published In

cover image Artificial Intelligence

Artificial Intelligence Volume 146, Issue 1

May 2003

121 pages

ISSN:0004-3702

Issue’s Table of Contents

Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 01 May 2003

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Cited By

Irfan MChan HSoundy JKiyavash NMooij J(2024)Equilibrium computation in multidimensional congestion gamesProceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence10.5555/3702676.3702758(1751-1779)Online publication date: 15-Jul-2024
https://dl.acm.org/doi/10.5555/3702676.3702758
Petrova ALarrosa J(2023)On Learning When to Decompose Graphical ModelsLearning and Intelligent Optimization10.1007/978-3-031-44505-7_19(270-285)Online publication date: 4-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-44505-7_19
Peruvemba Ramaswamy VSzeider S(2020)MaxSAT-Based Postprocessing for TreedepthPrinciples and Practice of Constraint Programming10.1007/978-3-030-58475-7_28(478-495)Online publication date: 7-Sep-2020
https://dl.acm.org/doi/10.1007/978-3-030-58475-7_28
Fichte JHecher MKieler M(2020)Treewidth-Aware Quantifier Elimination and Expansion for QCSPPrinciples and Practice of Constraint Programming10.1007/978-3-030-58475-7_15(248-266)Online publication date: 7-Sep-2020
https://dl.acm.org/doi/10.1007/978-3-030-58475-7_15
Habet DTerrioux CHung CPapadopoulos G(2019)Conflict history based search for constraint satisfaction problemProceedings of the 34th ACM/SIGAPP Symposium on Applied Computing10.1145/3297280.3297389(1117-1122)Online publication date: 8-Apr-2019
https://dl.acm.org/doi/10.1145/3297280.3297389
Lam WKask KLarrosa JDechter R(2018)Subproblem ordering heuristics for AND/OR best-first searchJournal of Computer and System Sciences10.1016/j.jcss.2017.10.00394:C(41-62)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1016/j.jcss.2017.10.003
Haddouch KEl moutaouakil KLazaar MTabii YChrayah MAl Achhab M(2017)New checker for constraint network solutionsProceedings of the 2nd international Conference on Big Data, Cloud and Applications10.1145/3090354.3090408(1-6)Online publication date: 29-Mar-2017
https://dl.acm.org/doi/10.1145/3090354.3090408
Jégou PTerrioux C(2017)Combining restarts, nogoods and bag-connected decompositions for solving CSPsConstraints10.1007/s10601-016-9248-822:2(191-229)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1007/s10601-016-9248-8
Amroun KHabbas ZAggoune-Mtalaa WMancini TMaratea MRicca F(2016)A compressed Generalized Hypertree Decomposition-based solving technique for non-binary Constraint Satisfaction ProblemsAI Communications10.3233/AIC-15069429:2(371-392)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.3233/AIC-150694
Karakashian SWoodward RChoueiry B(2013)Improving the performance of consistency algorithms by localizing and bolstering propagation in a tree decompositionProceedings of the Twenty-Seventh AAAI Conference on Artificial Intelligence10.5555/2891460.2891525(466-473)Online publication date: 14-Jul-2013
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