文章基本信息

标题：Approximating Partition Functions of Bounded-Degree Boolean Counting Constraint Satisfaction Problems
本地全文：下载
作者：Andreas Galanis ; Leslie Ann Goldberg ; Kuan Yang 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：80
页码：27:1-27:14
DOI：10.4230/LIPIcs.ICALP.2017.27
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We study the complexity of approximate counting Constraint Satisfaction Problems (#CSPs) in a bounded degree setting. Specifically, given a Boolean constraint language Gamma and a degree bound Delta, we study the complexity of #CSP_Delta(Gamma), which is the problem of counting satisfying assignments to CSP instances with constraints from Gamma and whose variables can appear at most Delta times. Our main result shows that: (i) if every function in Gamma is affine, then #CSP_Delta(Gamma) is in FP for all Delta, (ii) otherwise, if every function in Gamma is in a class called IM_2, then for all sufficiently large Delta, #CSP_Delta(Gamma) is equivalent under approximation-preserving (AP) reductions to the counting problem #BIS (the problem of counting independent sets in bipartite graphs) (iii) otherwise, for all sufficiently large Delta, it is NP-hard to approximate the number of satisfying assignments of an instance of #CSP_Delta(Gamma), even within an exponential factor. Our result extends previous results, which apply only in the so-called "conservative" case.
关键词：Constraint Satisfaction; Approximate Counting