The Complexity of Weighted Boolean #CSP

Date
Authors
Dyer, Martin
Goldberg, Leslie Ann
Jerrum, Mark
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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 parameterised by a finite set F of non-negative 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 the partition function, i.e. the sum of the weights of all configurations, can be computed in polynomial time if either (1) every function in F is of ``product type'', or (2) every function in F is ``pure affine''. For every other fixed set F, computing the partition function is FP^{#P}-complete.
Comment: Minor revision
Keywords
Computer Science - Computational Complexity, Mathematics - Combinatorics, F.2.2, F.4.1, G.2.1
Citation
Collections