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.
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This research was partially supported by the National 973 Program of China 2010CB328103 and the National Natural Science Foundation of China 60725207 and 60973033.
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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
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DOI: https://doi.org/10.1007/s11023-012-9270-6