Advertisement

Locally Consistent Constraint Satisfaction Problems

  • Zdeněk Dvořák
  • Daniel Král’
  • Ondřej Pangrác
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)

Abstract

An instance of a constraint satisfaction problem is l-consistent if any l constraints of it can be simultaneously satisfied. For a fixed constraint type P, ρ l (P) denotes the largest ratio of constraints which can be satisfied in any l-consistent instance. In this paper, we study locally consistent constraint satisfaction problems for constraints which are Boolean predicates. We determine the values of ρ l (P) for all l and all Boolean predicates which have a certain natural property which we call 1-extendibility as well as for all Boolean predicates of arity at most three. All our results hold for both the unweighted and weighted versions of the problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cook, S.: The Complexity of Theorem-proving Procedures. In: Proc. of the 3rd ACM Symposium on Theory of Computing, pp. 29–33. ACM, New York (1971)Google Scholar
  2. 2.
    Cook, S., Mitchell, D.: Finding Hard Instances of the Satisfiability Problem: A Survey. In: Satisfiability Problem: Theory and Applications. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 35, AMS, Providence (1997)Google Scholar
  3. 3.
    Eppstein, D.: Improved Algorithms for 3-coloring, 3-edge-coloring and Constraint Satisfaction. In: Proc. of the 12th ACM-SIAM Symposium on Discrete Algorithms, pp. 329–337. SIAM, Philadelphia (2001)Google Scholar
  4. 4.
    Feder, T., Motwani, R.: Worst-case Time Bounds for Coloring and Satisfiability Problems. J. Algorithms 45(2), 192–201 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hagerup, T., Rüb, C.: A guided tour Chernoff bounds. Inform. Process. Letters 33, 305–308 (1989)CrossRefGoogle Scholar
  6. 6.
    Huang, M.A., Lieberherr, K.: Implications of Forbidden Structures for Extremal Algorithmic Problems. Theoretical Computer Science 40, 195–210 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Jukna, S.: Extremal Combinatorics with Applications in Computer Science. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  8. 8.
    Král, D.: Locally Satisfiable Formulas. In: Proc. of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 323–332. SIAM, Philadelphia (2004)Google Scholar
  9. 9.
    Lieberherr, K., Specker, E.: Complexity of Partial Satisfaction. J. of the ACM 28(2), 411–422 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Lieberherr, K., Specker, E.: Complexity of Partial Satisfaction II. Technical Report 293, Dept. of EECS, Princeton University (1982)Google Scholar
  11. 11.
    Trevisan, L.: On Local versus Global Satisfiability. SIAM J. Disc. Math. (to appear); A preliminary version is available as ECCC report TR97-12Google Scholar
  12. 12.
    Usiskin, Z.: Max-min Probabilities in the Voting Paradox. Ann. Math. Stat. 35, 857–862 (1963)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Woeginger, G.J.: Exact Algorithms for NP-hard Problems: A Survey. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds.) Combinatorial Optimization - Eureka, You Shrink! LNCS, vol. 2570, pp. 185–207. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Yannakakis, M.: On the Approximation of Maximum Satisfiability. J. Algorithms 17, 475–502 (1994)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Zdeněk Dvořák
    • 1
  • Daniel Král’
    • 1
  • Ondřej Pangrác
    • 1
  1. 1.Department of Applied Mathematics and, Institute for Theoretical Computer Science (ITI)Charles UniversityPragueCzech Republic

Personalised recommendations