Variable-Centered Consistency in Model RB

Authors:
Liang Li;Tian Liu;Ke Xu
Affiliations:
Key Laboratory of High Confidence Software Technologies, School of Electronic Engineering and Computer Science, Ministry of Education, Institute of Software, Peking University, Beijing, China 1008 ...;Key Laboratory of High Confidence Software Technologies, School of Electronic Engineering and Computer Science, Ministry of Education, Institute of Software, Peking University, Beijing, China 1008 ...;National Laboratory of Software Development Environment, Beihang University, Beijing, China 100191
Venue:
Minds and Machines
Year:
2013

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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.