Chen, X, Dyer, M, Goldberg, LA et al. (4 more authors) (2013) The complexity of approximating conservative counting CSPs. In: Portier, N and Wilke, T, (eds.) Leibniz International Proceedings in Informatics, LIPIcs. 30th Symposium on Theoretical Aspects of Computer Science (STACS’13), 27 Feb - 02 Mar 2013, Kiel, Germany. Schloss Dagstuhl - Leibniz-Zentrum fur Informatik, Dagstuhl Publishing , pp. 148-159.
Abstract
We study the complexity of approximation for a weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, a classification is known for the Boolean domain. We give a classification for problems with general finite domain. We define weak log-modularity and weak log-supermodularity, and show that #CSP(F) is in FP if F is weakly log-modular. Otherwise, it is at least as hard to approximate as #BIS, counting independent sets in bipartite graphs, which is believed to be intractable. We further sub-divide the #BIS-hard case. If F is weakly log-supermodular, we show that #CSP(F) is as easy as Boolean log-supermodular weighted #CSP. Otherwise, it is NP-hard to approximate. Finally, we give a trichotomy for the arity-2 case. Then, #CSP(F) is in FP, is #BIS-equivalent, or is equivalent to #SAT, the problem of approximately counting satisfying assignments of a CNF Boolean formula.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | (c) Chen, Dyer, Goldberg, Jerrum, McQuillan, and Richerby; licensed under Creative Commons License BY-ND |
Keywords: | counting constraint satisfaction problem, approximation, complexity |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Jul 2016 15:37 |
Last Modified: | 11 Jul 2016 15:37 |
Published Version: | http://doi.org/10.4230/LIPIcs.STACS.2013.148 |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum fur Informatik, Dagstuhl Publishing |
Identification Number: | 10.4230/LIPIcs.STACS.2013.148 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89274 |