The complexity of weighted and unweighted #CSP
Andrei Bulatov, Martin Dyer, Leslie Ann Goldberg, Markus Jalsenius,, Mark Jerrum, David Richerby
TL;DR
This paper explores the computational complexity of weighted and unweighted #CSP problems, providing reductions that extend existing dichotomy results to rational-weighted cases for both exact and approximate computations.
Contribution
It introduces reductions among weighted #CSP problems that broaden the applicability of unweighted #CSP dichotomy results to rational weights.
Findings
Extended the unweighted #CSP dichotomy to rational-weighted #CSP.
Provided reductions applicable to both exact and approximate #CSP computations.
Clarified the complexity landscape of weighted and unweighted #CSP problems.
Abstract
We give some reductions among problems in (nonnegative) weighted #CSP which restrict the class of functions that needs to be considered in computational complexity studies. Our reductions can be applied to both exact and approximate computation. In particular, we show that a recent dichotomy for unweighted #CSP can be extended to rational-weighted #CSP.
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