The Complexity of Weighted Boolean #CSP
Computational Complexity
2009-02-23 v2 Combinatorics
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 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.
Cite
@article{arxiv.0704.3683,
title = {The Complexity of Weighted Boolean #CSP},
author = {Martin Dyer and Leslie Ann Goldberg and Mark Jerrum},
journal= {arXiv preprint arXiv:0704.3683},
year = {2009}
}