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标题：Bounds on the Satisfiability Threshold for Power Law Distributed Random SAT
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作者：Tobias Friedrich ; Anton Krohmer ; Ralf Rothenberger 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：87
页码：37:1-37:15
DOI：10.4230/LIPIcs.ESA.2017.37
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the development of sophisticated rigorous and non-rigorous techniques for analyzing random structures. Despite a long line of research and substantial progress, nearly all theoretical work on random SAT assumes a uniform distribution on the variables. In contrast, real-world instances often exhibit large fluctuations in variable occurrence. This can be modeled by a scale-free distribution of the variables, which results in distributions closer to industrial SAT instances. We study random k-SAT on n variables, m = Theta(n) clauses, and a power law distribution on the variable occurrences with exponent beta. We observe a satisfiability threshold at beta = (2k-1)/(k-1). This threshold is tight in the sense that instances with beta 0 are unsatisfiable with high probability (w.h.p.). For beta >= (2k-1)/(k-1)+epsilon, the picture is reminiscent of the uniform case: instances are satisfiable w.h.p. for sufficiently small constant clause-variable ratios m/n; they are unsatisfiable above a ratio m/n that depends on beta.
关键词：satisfiability; random structures; random SAT; power law distribution; scale-freeness; phase transitions