Year: 2009
Type: article
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 $\mathcal{F}$ 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 $\text{{\sf FP}}^{\text{{\sf#P}}}$-complete unless either (1) every function in $\mathcal{F}$ is of “product type,” or (2) every function in $\mathcal{F}$ is “pure affine.” In the remaining cases, computing the partition function is in P.
Source: SIAM Journal on Computing
DOI: 10.1137/070690201
Authors: Martin Dyer, Leslie Ann Goldberg, Mark Jerrum
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G3228783945, G4478843088, G7248835559
OpenAlex ID: W2097738137