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The complexity of weighted boolean #CSP*

Dyer, M., Goldberg, L.A. and Jerrum, M. (2009) The complexity of weighted boolean #CSP*. Siam Journal on Computing, 38 (5). pp. 1970-1986. ISSN 0097-5397

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Abstract

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterized by a finite set F of nonnegative functions that may be used to assign weights to the configurations (feasible solutions) of a problem instance. Classical constraint satisfaction problems correspond to the special case of 0,1-valued functions. We show that computing the partition function, i.e., the sum of the weights of all configurations, is FP#P-complete unless either (1) every function in F is of “product type,” or (2) every function in F is “pure affine.” In the remaining cases, computing the partition function is in P.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009 Society for Industrial and Applied Mathematics. Reproduced with permission from the publisher.
Keywords: complexity theory, counting, #P, constraint satisfaction
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Miss Jamie Grant
Date Deposited: 20 Mar 2009 13:55
Last Modified: 06 Jun 2014 23:16
Published Version: http://dx.doi.org/10.1137/070690201
Status: Published
Publisher: SIAM Society for Industrial and Applied Mathematics
Refereed: Yes
Identification Number: 10.1137/070690201
URI: http://eprints.whiterose.ac.uk/id/eprint/7981

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