---
res:
bibo_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.
Finite-valued constraint languages contain functions that take on rational costs
and general-valued constraint languages contain functions that take on rational
or infinite costs. An instance of the problem is specified by a sum of 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).\r\nOur main result is a precise algebraic characterisation
of valued constraint languages whose instances can be solved exactly by the basic
linear programming relaxation (BLP). For a general-valued constraint language
Γ, BLP is a decision procedure for Γ if and only if Γ admits a symmetric fractional
polymorphism of every arity. For a finite-valued constraint language Γ, BLP is
a decision procedure if and only if Γ admits a symmetric fractional polymorphism
of some arity, or equivalently, if Γ admits a symmetric fractional polymorphism
of arity 2.\r\nUsing these results, we obtain tractability of several novel and
previously widely-open classes of VCSPs, including problems over valued constraint
languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also
known as k-submodular) on arbitrary finite domains; (3) weakly (and hence strongly)
tree-submodular on arbitrary trees. @eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Vladimir
foaf_name: Kolmogorov, Vladimir
foaf_surname: Kolmogorov
foaf_workInfoHomepage: http://www.librecat.org/personId=3D50B0BA-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Johan
foaf_name: Thapper, Johan
foaf_surname: Thapper
- foaf_Person:
foaf_givenName: Stanislav
foaf_name: Živný, Stanislav
foaf_surname: Živný
bibo_doi: 10.1137/130945648
bibo_issue: '1'
bibo_volume: 44
dct_date: 2015^xs_gYear
dct_language: eng
dct_publisher: SIAM@
dct_title: The power of linear programming for general-valued CSPs@
...