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DOI: 10.4230/LIPIcs.ICALP.2017.27
URN: urn:nbn:de:0030-drops-74099
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7409/
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Galanis, Andreas ; Goldberg, Leslie Ann ; Yang, Kuan

Approximating Partition Functions of Bounded-Degree Boolean Counting Constraint Satisfaction Problems

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Abstract

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.

BibTeX - Entry

@InProceedings{galanis_et_al:LIPIcs:2017:7409,
  author =	{Andreas Galanis and Leslie Ann Goldberg and Kuan Yang},
  title =	{{Approximating Partition Functions of Bounded-Degree Boolean Counting Constraint Satisfaction Problems}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7409},
  URN =		{urn:nbn:de:0030-drops-74099},
  doi =		{10.4230/LIPIcs.ICALP.2017.27},
  annote =	{Keywords: Constraint Satisfaction, Approximate Counting}
}

Keywords: Constraint Satisfaction, Approximate Counting
Seminar: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 06.07.2017


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