The complexity of general-valued CSPs seen from the other side
Abstract
The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias, Bulatov, and Dalmau [ICALP'07] establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by bounded-consistency algorithms (unconditionally) as bounded treewidth modulo homomorphic equivalence. The general-valued constraint satisfaction problem (VCSP) is a generalisation of the CSP concerned with homomorphisms between two valued structures. For VCSPs with restricted left-hand side valued structures, we establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by the -th level of the Sherali-Adams LP hierarchy (unconditionally). We also obtain results on related problems concerned with finding a solution and recognising the tractable cases; the latter has an application in database theory.
Keywords
Cite
@article{arxiv.1710.03148,
title = {The complexity of general-valued CSPs seen from the other side},
author = {Clement Carbonnel and Miguel Romero and Stanislav Zivny},
journal= {arXiv preprint arXiv:1710.03148},
year = {2022}
}
Comments
v3: Full version of a FOCS'18 paper; some parts shortened compared to v2 and other small corrections