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DOI: 10.4230/LIPIcs.ICALP.2017.27
URN: urn:nbn:de:0030-drops-74099
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7409/
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: | 07.07.2017 |
