Skip to main content
SpringerLink
Log in

Variable-Centered Consistency in Model RB

  • Published:
Minds and Machines Aims and scope Submit manuscript

Abstract

Model RB is a model of random constraint satisfaction problems, which exhibits exact satisfiability phase transition and many hard instances, both experimentally and theoretically. Benchmarks based on Model RB have been successfully used by various international algorithm competitions and many research papers. In a previous work, Xu and Li defined two notions called i-constraint assignment tuple and flawed i-constraint assignment tuple to show an exponential resolution complexity of Model RB. These two notions are similar to some kind of consistency in constraint satisfaction problems, but seem different from all kinds of consistency so far known in literatures. In this paper, we explicitly define this kind of consistency, called variable-centered consistency, and show an upper bound on a parameter in Model RB, such that up to this bound the typical instances of Model RB are variable-centered consistent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bessiere, C. (2006). Constraint propagation, handbook of constraint programming (pp. 29–84).

  • Cai, S., Su, K., & Sattar, A. (2011). Local search with edge weighting and configuration checking heuristics for minimum vertex cover. Artificial Intelligence, 175(9–10), 1672–1696.

    Article  MathSciNet  MATH  Google Scholar 

  • Cheeseman, P., Kanefsky, R., & Taylor, W. (1991). Where the really hard problems are. In Proceedings of IJCAI (pp. 163–169).

  • Dechter, R. (2003). Constraint processing. San Mateo, CA: Morgan Kaufmann.

    Google Scholar 

  • Fan, Y., & Shen, J. (2011). On the phase transitions of random k-constraint satisfaction problems. Artificial Intelligence, 175, 914–927.

    Article  MathSciNet  MATH  Google Scholar 

  • Freuder, E. C. (1982). A sufficient condition for backtrack-free search. Journal of the Association for Computing Machinery, 29(1), 24–32.

    Article  MathSciNet  MATH  Google Scholar 

  • Gao, Y., & Culberson, J. C. (2007). Consistency and random constraint satisfaction models. Journal of Artificial Intelligence Research, 28, 517–557.

    MathSciNet  MATH  Google Scholar 

  • Gomes, C., & Walsh, T. (2006). Randomness and structures, handbook of constraint programming (pp. 639–664).

  • Janson, S., Luczak, T., & Rucinski, A. (2000). Random graphs. New York: Wiley.

    Book  MATH  Google Scholar 

  • Lecoutre, C. (2009). Constraint networks: Techniques and algorithms. New York: ISTE/Wiley.

    Book  Google Scholar 

  • Li, W. (2010). Logical verification of scientific discovery. Science China Information Sciences, 53(4), 677–684.

    Article  MathSciNet  Google Scholar 

  • Liu, T., Lin, X., Wang, C., Su, K., & Xu, K. (2011). Large hinge width on sparse random hypergraphs. In Proceedings of the 22nd international joint conference on artificial intelligence (IJCAI’2011) (pp. 611–616).

  • Luo, J., & Li, W. (2011). An algorithm to compute maximal contractions for Horn clauses. Science China Information Sciences, 54(2), 244–257.

    Article  MathSciNet  MATH  Google Scholar 

  • Mackworth, A. K. (1977). Consistency in networks of relations. Artificial Intelligence, 8, 99–118.

    Article  MATH  Google Scholar 

  • Mitzenmacher, M., & Upfal, E. (2005). Probability and computing. Cambridge, UK: Cambridge University Press.

    MATH  Google Scholar 

  • Montanari, U. (1974). Networks of constraints: Fundamental properties and applications to picture processing. Information sciences, 7, 95–132.

    Article  MathSciNet  MATH  Google Scholar 

  • Tsang, E. P. K. (1993). Foundations of constraint satisfaction. London and San Diego: Academic Press.

    Google Scholar 

  • Xu, K. (2004). BHOSLIB: Benchmarks with hidden optimum solutions for graph problems. http://www.nlsde.buaa.edu.cn/kexu/benchmarks/graph-benchmarks.htm.

  • Xu, K., & Li, W. (2000). Exact phase transitions in random constraint satisfaction problems. Journal of Artificial Intelligence Research, 12, 93–103.

    MathSciNet  MATH  Google Scholar 

  • Xu, K., & Li, W. (2006). Many hard examples in exact phase transitions. Theoretical Computer Science, 355, 291–302.

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, K., Boussemart, F., Hemery, F., & Lecoutre, C. (2007). Random constraint satisfaction: Easy generation of hard (satisfiable) instances. Artificial Intelligence, 171, 514–534.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This research was partially supported by the National 973 Program of China 2010CB328103 and the National Natural Science Foundation of China 60725207 and 60973033.

Author information

Authors and Affiliations

  1. Key Laboratory of High Confidence Software Technologies, School of Electronic Engineering and Computer Science, Ministry of Education, Institute of Software, Peking University, Beijing, 100871, China

    Liang Li & Tian Liu

  2. National Laboratory of Software Development Environment, Beihang University, Beijing, 100191, China

    Ke Xu

Authors
  1. Liang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ke Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Tian Liu or Ke Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, L., Liu, T. & Xu, K. Variable-Centered Consistency in Model RB. Minds & Machines 23, 95–103 (2013). https://doi.org/10.1007/s11023-012-9270-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11023-012-9270-6

Keywords

Search

Navigation