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Network-Based Heuristics for Constraint-Satisfaction Problems

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Search in Artificial Intelligence

Part of the book series: Symbolic Computation ((1064))

Abstract

Many AI tasks can be formulated as Constraint-Satisfaction problems (CSP), i.e., the assignment of values to variables subject to a set of constraints. While some CSPs are hard, those that are easy can often be mapped into sparse networks of constraints which, in the extreme case, are trees. This paper identifies classes of problems that lend themselves to easy solutions, and develops algorithms that solve these problems optimally. The paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree-structured CSPs. The advice is generated by simplifying the pending subproblems into trees, counting the number of consistent solutions in each simplified subproblem, and comparing these counts to decide among the choices pending in the original problem.

This work was supported in part by the National Science Foundation, Grant #DCR 85-01234

This paper is a revision of one that first appeared in the Journal of Artificial Intelligence, V34, 1988, and is reprinted here by permission of the publisher, North-Holland Publishing Co. Amsterdam.

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References

  1. S. Amborg, “Efficient algorithms for combinatorial problems on graphs with bounded decomposability–a survey,” BIT, Vol. 25, 1985, pp. 2–23.

    MathSciNet  Google Scholar 

  2. S. Amborg, D. G. Cornell, and A. Proskurowski, “Complexity of finding embeddings in a k-tree,” Siam Journal of algorithm and Discrete Math.,Vol. 8, No. 2, 1987., pp. 277–184.

    Article  Google Scholar 

  3. U. Bertele and F. Brioschi, Nonserial Dynamic Programming, New York: Academic press, 1972.

    MATH  Google Scholar 

  4. Maurice Bruynooghe and Luis M. Pereira, “Deduction Revision by Intelligent backtracking,” in Implementation of Prolog, J.A. Campbell, Ed. Ellis Harwood, 1984, pp. 194–215.

    Google Scholar 

  5. J.G. Carbonell, “Learning by analogy: Formulation and generating plan from past experience,” in Machine Learning, Michalski, Carbonell and Mitchell, Ed. Palo Alto, California: Tioga Press, 1983.

    Google Scholar 

  6. P.T. Cox, “Finding backtrack points for intelligent backtracking,” in Implementation of Prolog, J.A. Campbell, Ed. Ellis Harwood, 1984, pp. 216–233.

    Google Scholar 

  7. R. Dechter and J.Pearl, “A problem simplification approach that generates heuristics for constraint satisfaction problems.,” UCLA-Eng-rep.8497. To appear in Machine Intelligence 11., 1985.

    Google Scholar 

  8. R. Dechter and J. Pearl, “The anatomy of easy problems: a constraint-satisfaction formulation,” in Proceedings Ninth International Conference on Artificial Intelligence, Los Angeles, Cal: 1985, pp. 1066–1072.

    Google Scholar 

  9. R. Dechter, “Learning while searching in constraintsatisfaction-problems,” in Proceedings AAAI-86, Philadelphia, Pensilvenia: 1986.

    Google Scholar 

  10. A. Dechter and R. Dechter, “Removing redundencies in constraint networks,” in Proceedings AAAI-87, Seattle, Washington: 1987

    Google Scholar 

  11. Rina Dechter, “Tree-Clustering Schemes for Constraint-Processing,” Cognitive Systems Laboratory, Tech. Rep. (R-92), 1987.

    Google Scholar 

  12. R. Dechter and J. Pearl, “The cycle-cutset method for improving search performance in AI applications,” in Proceeding of the 3rd IEEE on AI Applications, Orlando, Florida: 1987.

    Google Scholar 

  13. John Doyle, “A truth maintenance system,” Artificial Intelligence, Vol. 12, 1979, pp. 231–272.

    Article  MathSciNet  Google Scholar 

  14. S. Even, Graph Algorithms, Maryland, USA: Computer Science Press, 1979.

    MATH  Google Scholar 

  15. E.C. Freuder, “A sufficient condition of backtrack-free search.,” Journal of the ACM, Vol. 29, No. 1, 1982, pp. 24–32.

    Article  MathSciNet  MATH  Google Scholar 

  16. E.C. Freuder, “A sufficient condition for backtrack-bounded search,” Journal of the Association of Computing Machinery, Vol. 32, No. 4, 1985, pp. 755–761.

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Gaschnig, “Performance measurement and analysis of certain search algorithms.,” Carnegie-Mellon University, Pitsburg, Pensilvenia, Tech. Rep. CMU-CS79–124, 1979.

    Google Scholar 

  18. J. Gaschnig, “A problem similarity approach to devising heuristics: first results,” in Proceedings 6th international joint conf. on Artificial Intelligence., Tokyo, Jappan: 1979, pp. 301–307.

    Google Scholar 

  19. G. Guida and M. Somalvico, “A method for computing heuristics in problem solving,” Information Sciences, Vol. 19, 1979, pp. 251–259.

    Article  MathSciNet  MATH  Google Scholar 

  20. R. M. Haralick and G.L. Elliot, “Increasing tree search efficiency for constraint satisfaction problems,” AI Journal, Vol. 14, 1980, pp. 263–313.

    Google Scholar 

  21. D. E. Knuth, “Esimating the efficiency of backtrack programs,” Mathematics of computation, Vol. 29, No. 129, 1975, pp. 121–136.

    Article  MathSciNet  MATH  Google Scholar 

  22. A.K. Mackworth, “Consistency in networks of relations,” Artifficial intelligence, Vol. 8, No. 1, 1977, pp. 99–118.

    Article  MATH  Google Scholar 

  23. A.K. Mackworth and E.C. Freuder, “The complexity of some polynomial network consistancy algorithms for constraint satisfaction problems,” Artificial Intelligence, Vol. 25, No. 1, 1984.

    Google Scholar 

  24. Joao P. Martins and Stuart C. Shapiro, “Theoretical Foundations for belief revision,” in Proceedings Theoretical aspects of Reasoning about knowledge, 1986.

    Google Scholar 

  25. Stanislaw Matwin and Tomasz Pietrzykowski, “Intelligent backtracking in plan-based deduction,” IEEE Transaction on Pattern Analysis and Machine Intelligence,Vol. PAMI-7, No. 6, 1985, pp. 682–692.

    Article  MATH  Google Scholar 

  26. M. Minsky, “Steps towards Artificial Intelligence,” in Computer and Thought, Feigenbaoum Feldman, Ed. McGraw-Hill, 1963, p. 442.

    Google Scholar 

  27. R. Mohr and T.C. Henderson, “Arc and Path consistency revisited,” Artificial Intelligence, Vol. 28, No. 2, 1986, pp. 225–233.

    Article  Google Scholar 

  28. U. Montanari, “Networks of constraints:fundamental properties and applications to picture processing,” Information Science, Vol. 7, 1974, pp. 95–132.

    Article  MathSciNet  Google Scholar 

  29. B. Nudel, “Consistent-Labeling problems and their algorithms. Expected complexities and theory based heuristics.,” Artificial Intelligence, Vol. 21, 1983, pp. 135–178.

    Article  Google Scholar 

  30. J. Pearl, “On the discovery and generation of certain heuristics,” AI Magazine, No. 22–23, 1983.

    Google Scholar 

  31. P. Purdom, “Search rearrangement backtracking and polynomial average time,” AI Journal, Vol. 21, 1983, pp. 117–133.

    Google Scholar 

  32. P.W. Purdom and C.A. Brown, The Analysis of Algorithms: CBS College Publishing, Holt, Rinehart and Winston, 1985.

    Google Scholar 

  33. E. D. Sacerdoti, “Planning in a hierarchy of abstraction spaces,” Artificial Intelligence, Vol. 5, No. 2, 1974, pp. 115–135.

    Article  MATH  Google Scholar 

  34. R.M. Stallman and G. J. Sussman, “Forward reasoning and dependency-directed backtracking in a system for computer-aided circuit analysis,” Artificial Intelligence, Vol. 9, No. 2, 1977, pp. 135–196.

    Article  MATH  Google Scholar 

  35. H. S. Stone and J. M. Stone, “Efficient search techniques- An empirical study of the N-queens problem.,” IBM T.J. Watson Research Center, Yorktown Heights,NY Tech. Rep. RC12057 (54343) 1986.

    Google Scholar 

  36. H.S. Stone and P. Sipala, “The average complexity of depth-first search with backtracking and cut-off,” IBM JRD, Vol. 30, No. 3, 1986, pp. 242–258.

    Article  MATH  Google Scholar 

  37. R. Tarjan and M. Yannakakis, “Simple Linear-Time Alsorithms to test Chordality of graphs, test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs,” SIAM Journal of Computing, Vol. 13, No. 3, 1984, pp. 566–579.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Cognitive Systems Laboratory, Computer Science Department, University of California, Los Angeles, CA, 90024-1596, USA

    Rina Dechter & Judea Pearl

  2. Artificial Intelligence Center, Hughes Aircraft Company, Calabasas, CA, 91302, USA

    Rina Dechter

Authors
  1. Rina Dechter
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  2. Judea Pearl
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Maryland, 20742, College Park, MD, USA

    Laveen Kanal

  2. Computer Science Department, University of Texas at Austin, 78712-1188, Austin, TX, USA

    Vipin Kumar

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© 1988 Springer-Verlag New York Inc.

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Dechter, R., Pearl, J. (1988). Network-Based Heuristics for Constraint-Satisfaction Problems. In: Kanal, L., Kumar, V. (eds) Search in Artificial Intelligence. Symbolic Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8788-6_11

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  • DOI: https://doi.org/10.1007/978-1-4613-8788-6_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8790-9

  • Online ISBN: 978-1-4613-8788-6

  • eBook Packages: Springer Book Archive

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