The complexity of weighted and unweighted #CSP

Authors:
Andrei Bulatov;Martin Dyer;Leslie Ann Goldberg;Markus Jalsenius;Mark Jerrum;David Richerby
Affiliations:
School of Computing Science, Simon Fraser University, University Drive, Burnaby, Canada, V5A 1S6;School of Computing, University of Leeds, Leeds, LS2 9JT, UK;Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK;Department of Computer Science, University of Bristol, Bristol, BS8 1UB, UK;School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK;Department of Computer Science, University of Liverpool, Liverpool, L69 3BX, UK
Venue:
Journal of Computer and System Sciences
Year:
2012

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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 the recent dichotomy for unweighted #CSP can be extended to rational-weighted #CSP.