An empirical study of Max-2-sat phase transitions.

*(English)*Zbl 1179.68148
Kranakis, Evangelos (ed.) et al., Typical case complexity and phase transitions. Papers from the workshop, Ottawa, ON, Canada, May 14–16, 2003. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 16, 80-92 (2003).

Summary: The decision version of the maximum satisfiability problem (MAX-SAT) is stated as follows: Given a set \(S\) of propositional clauses and an integer \(g\), decide if there exists a truth assignment that falsifies at most \(g\) clauses in \(S\), where g is called the allowance for false clauses. We conduct an extensive experiment on over a million of random instances of 2-SAT and identify statistically the relationship between \(g, n\) (number of variables) and m (number of clauses). In our experiment, we apply an efficient decision procedure based on the branch-and-bound method. The statistical data of the experiment confirm not only the “scaling window” of MAX-2-SAT discovered by Chayes, Kim and Borgs, but also the recent results of Coppersmith et al. While there is no easy-hard-easy pattern for the complexity of 2-SAT at the phase transition, we show that there is such a pattern for the decision problem of MAX-2-SAT associated with the phase transition. We also identify that the hardest problems are among those with high allowance for false clauses but low number of clauses.

For the entire collection see [Zbl 1109.68315].

For the entire collection see [Zbl 1109.68315].

##### MSC:

68T20 | Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) |

##### Software:

MAX-2-SAT
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\textit{H. Shen} and \textit{H. Zhag}, Electron. Notes Discrete Math. 16, 80--92 (2003; Zbl 1179.68148)

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##### References:

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