Chen, X, Dyer, M orcid.org/0000-0002-2018-0374, Goldberg, LA et al. (4 more authors) (2015) The complexity of approximating conservative counting CSPs. Journal of Computer and System Sciences, 81 (1). pp. 311-329. ISSN 0022-0000
Abstract
We study the complexity of the approximate weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, a classification is known over the Boolean domain; we extend this to arbitrary finite domains. We show that if F is "weakly log-modular", then #CSP(F) is in FP. Otherwise, it is at least as difficult to approximate as #BIS (counting independent sets in bipartite graphs). #BIS is complete for the complexity class #RHΠ1, and believed to be intractable. We further sub-divide the #BIS-hard case: if F is "weakly log-supermodular", #CSP(F) is as easy as a Boolean log-supermodular weighted #CSP; otherwise, we show that it is NP-hard to approximate. Finally, we give a full trichotomy for the arity-2 case: #CSP(F) is in FP, is #BIS-equivalent, or is equivalent to #SAT (approximately counting the satisfying assignments of Boolean CNF formulas). We also discuss algorithmic aspects of our classification.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2014 Elsevier Inc. All rights reserved. This is an author produced version of a paper published in Journal of Computer and System Sciences. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Approximation; Counting complexity; Constraint satisfaction problems |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Oct 2015 15:39 |
Last Modified: | 03 Dec 2020 18:30 |
Published Version: | http://dx.doi.org/10.1016/j.jcss.2014.06.006 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jcss.2014.06.006 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89268 |