Year: 2012
Type: conference-paper
Abstract: A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. This framework includes and generalises well-studied constraint satisfaction problems (CSPs) and maximum constraint satisfaction problems (Max-CSPs). Our main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation. Using this result, we obtain tractability of several novel and previously widely-open classes of VCSPs, including problems over valued constraint languages that are: (1) sub modular on arbitrary lattices, (2) bisubmodular (also known as k-sub modular) on arbitrary finite domains, (3) weakly (and hence strongly) tree-sub modular on arbitrary trees.
DOI: 10.1109/focs.2012.25
Authors: Johan Thapper, Stanislav Zivny
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2138514146