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 |
| 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: | 08 Feb 2013 17:06 |
| 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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