Advertisement

Formal Models of Heavy-Tailed Behavior in Combinatorial Search

  • Hubie Chen
  • Carla Gomes
  • Bart Selman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2239)

Abstract

Recently, it has been found that the cost distributions of randomized backtrack search in combinatorial domains are often heavytailed. Such heavy-tailed distributions explain the high variability observed when using backtrack-style procedures. A good understanding of this phenomenon can lead to better search techniques. For example, restart strategies provide a good mechanism for eliminating the heavytailed behavior and boosting the overall search performance. Several state-of-the-art SAT solvers now incorporate such restart mechanisms. The study of heavy-tailed phenomena in combinatorial search has so far been been largely based on empirical data. We introduce several abstract tree search models, and show formally how heavy-tailed cost distribution can arise in backtrack search. We also discuss how these insights may facilitate the development of better combinatorial search methods.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Bayardo and R. Schrag. Using csp look-back techniques to solve real-world sat instances. In Proc. of the 14th Natl. Conf. on Arti.cial Intelligence (AAAI-97), pages 203–208, New Providence, RI, 1997. AAAI Press.Google Scholar
  2. 2.
    J. M. Crawford, M. J. Kearns, and R. E. Schapire. The minimal disagreement parity problem as a hard satisfiability problem. Technical report (also in dimacs sat benchmark), CIRL, 1994.Google Scholar
  3. 3.
    C. Gomes, B. Selman, and N. Crato. Heavy-tailed Distributions in Combinatorial Search. In G. Smolka, editor, Princp. and practice of Constraint Programming (CP97). Lect. Notes in Comp. Sci., pages 121–135. Springer-Verlag, 1997.Google Scholar
  4. 4.
    C. Gomes, B. Selman, and H. Kautz. Boosting Combinatorial Search Through Randomization. In Proceedings of the Fifteenth National Conference on Artificial Intelligence (AAAI-98), pages 431–438, New Providence, RI, 1998. AAAI Press.Google Scholar
  5. 5.
    C. P. Gomes, B. Selman, N. Crato, and H. Kautz. Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. J. of Automated Reasoning, 24(1–2):67–100, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    M. Harchol-Balter, M. Crovella, and C. Murta. On choosing a task assignment policy for a distributed server system. In Proceedings of Performance Tools’ 98, pages 231–242. Springer-Verlag, 1998.Google Scholar
  7. 7.
    I. Jacobs and E. Berlekamp. A lower bound to the distribution of computation for sequential decoding. IEEE Trans. Inform. Theory, pages 167–174, 1963.Google Scholar
  8. 8.
    C. M. Li. A constrained-based approach to narrow search trees for satisfiability. Information processing letters, 71:75–80, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    C. M. Li and Anbulagan. Heuristics based on unit propagation for satisfiability problems. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 366–371. AAAI Pess, 1997.Google Scholar
  10. 10.
    M. Luby, A. Sinclair, and D. Zuckerman. Optimal speedup of las vegas algorithms. Information Process. Letters, pages 173–180, 1993.Google Scholar
  11. 11.
    J. P. Marques-Silva and K. A. Sakallah. Grasp-a search algorithm for propositional satisfiability. IEEE Transactions on Computers, 48(5):506–521, 1999.CrossRefMathSciNetGoogle Scholar
  12. 12.
    M. Moskewicz, C. Madigan, Y. Zhao, L. Zhang, and S. Malik. Chaff: Engineering an efficient sat solver. In Proc. of the 39th Design Automation Conf., 2001.Google Scholar
  13. 13.
    T. Walsh. Search in a small world. In IJCAI-99, 1999.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Hubie Chen
    • 1
  • Carla Gomes
    • 1
  • Bart Selman
    • 1
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA

Personalised recommendations