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Local and global relational consistency

  • Constraint Satisfaction Problems 2
  • Conference paper
  • First Online:
Principles and Practice of Constraint Programming — CP '95 (CP 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 976))

Abstract

Local consistency has proven to be an important concept in the theory and practice of constraint networks. In this paper, we present a new definition of local consistency, called relational consistency. The new definition is relationbased, in contrast with the previous definition of local consistency, which we characterize as variable-based. It allows the unification of known elimination operators such as resolution in theorem proving, joins in relational databases and variable elimination for solving linear inequalities. We show the usefulness and conceptual power of the new definition in characterizing relationships between four properties of constraints — domain tightness, row-convexity, constraint tightness, and constraint looseness — and the level of local consistency needed to ensure global consistency. As well, algorithms tor enforcing relational consistency are introduced and analyzed.

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References

  1. S. Arnborg, D. G. Corneil, and A. Proskurowski. Complexity of finding an embedding in k-trees. SIAM Journal of Algebraic Discrete Methods, 8:177–184, 1987.

    Google Scholar 

  2. C. Beeri, R. Fagin, D. Maier, and M. Yannakakis. On the desirability of acyclic database schemes. J. ACM, 30:479–513, 1983.

    Article  Google Scholar 

  3. M. C. Cooper. An optimal k-consistency algorithm. Artif. Intell., 41:89–95, 1989.

    Article  Google Scholar 

  4. M. Davis and H. Putnam. A computing procedure for quantification theory. J. ACM, 7:201–215, 1960.

    Article  Google Scholar 

  5. R. Dechter. From local to global consistency. Artif. Intell., 55:87–107, 1992.

    Article  Google Scholar 

  6. R. Dechter, I. Meiri, and J. Pearl. Temporal constraint networks. Artif. Intell., 49:61–95, 1991.

    MathSciNet  Google Scholar 

  7. R. Dechter and J. Pearl. Network-based heuristics for constraint satisfaction problems. Artif. Intell., 34:1–38, 1988.

    Article  Google Scholar 

  8. R. Dechter and J. Pearl. Tree clustering for constraint networks. Artif. Intell., 38:353–366, 1989.

    Article  Google Scholar 

  9. R. Dechter and J. Pearl. Directed constraint networks: A relational framework for causal modeling. In Proc. of the 12th Int'l Joint Conf. on AI, pages 1164–1170, 1991.

    Google Scholar 

  10. R. Dechter and I. Rish. Directional resolution: The Davis-Putnam procedure, revisited. In Proc. of the 4th Int'l Conf. on Principles of KR&R, 1994.

    Google Scholar 

  11. E. C. Freuder. Synthesizing constraint expressions. Comm. ACM, 21:958–966, 1978.

    Article  Google Scholar 

  12. E. C. Freuder. A sufficient condition for backtrack-free search. J. ACM, 29:24–32, 1982.

    Article  Google Scholar 

  13. M. L. Ginsberg, M. Frank, M. P. Halpin, and M. C. Torrance. Search lessons learned from crossword puzzles. In Proc. of the 8th Nat'l Conf. on AI, pages 210–215, 1990.

    Google Scholar 

  14. P. Jégou. On the consistency of general constraint satisfaction problems. In Proc. of the 11th National Conf. on AI, pages 114–119, 1993.

    Google Scholar 

  15. L. M. Kirousis. Fast parallel constraint satisfaction. Artif. Intell., 64:147–160, 1993.

    Article  Google Scholar 

  16. J-L Lassez and M. Mahler, “On Fourier's algorithm for linear constraints” Journal of Automated Reasoning, Vol 9, 1992.

    Google Scholar 

  17. A. K. Mackworth. Consistency in networks of relations. Artif. Intell., 8:99–118, 1977.

    Article  Google Scholar 

  18. A. K. Mackworth and E. C. Freuder. The complexity of some polynomial network consistency algorithms for constraint satisfaction problems. Artif. Intell., 25:65–74, 1985.

    Article  Google Scholar 

  19. D. Maier. The Theory of Relational Databases. Computer Science Press, 1983.

    Google Scholar 

  20. U. Montanari. Networks of constraints: Fundamental properties and applications to picture processing. Inform. Sci., 7:95–132, 1974.

    Article  Google Scholar 

  21. B. A. Nadel. Constraint satisfaction algorithms. Comput. Intell., 5:188–224, 1989.

    Google Scholar 

  22. P. van Beek. On the minimality and decomposability of constraint networks. In Proc. of the 10th National Conf. on AI, pages 447–452, 1992.

    Google Scholar 

  23. P. van Beek. On the inherent level of local consistency in constraint networks. In Proc. of the 12th National Conf. on AI, pages 368–373, 1994.

    Google Scholar 

  24. P. van Beek and R. Dechter. Constraint tightness versus global consistency. In Proc. of the 4th Int'l Conf. on Principles of KR&R, pages 572–582, 1994.

    Google Scholar 

  25. P. van Beek and R. Dechter. On the minimality and global consistency of rowconvex constraint networks. To appear in J. ACM, 1995.

    Google Scholar 

  26. P. Van Hentenryck, Y. Deville, and C.-M. Teng. A generic arc consistency algorithm and its specializations. Artif. Intell., 57:291–321, 1992.

    Article  Google Scholar 

  27. M. Vilain and H. Kautz. Constraint propagation algorithms for temporal reasoning. In Proc. of the 5th National Conf. on AI, pages 377–382, 1986.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Information and Computer Science, University of California, 92717, Irvine Irvine, California, USA

    Rina Dechter

  2. Department of Computing Science, University of Alberta, T6G 2H1, Edmonton, Alberta, Canada

    Peter van Beek

Authors
  1. Rina Dechter
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  2. Peter van Beek
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Editor information

Ugo Montanari Francesca Rossi

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© 1995 Springer-Verlag Berlin Heidelberg

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Dechter, R., van Beek, P. (1995). Local and global relational consistency. In: Montanari, U., Rossi, F. (eds) Principles and Practice of Constraint Programming — CP '95. CP 1995. Lecture Notes in Computer Science, vol 976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60299-2_15

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  • DOI: https://doi.org/10.1007/3-540-60299-2_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60299-6

  • Online ISBN: 978-3-540-44788-7

  • eBook Packages: Springer Book Archive

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