The Complexity of General-Valued CSPs Seen from the Other Side

Clement Carbonnel, Miguel Romero, Stanislav Zivny
2018 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)  
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 algorithm (unconditionally) as bounded treewidth modulo homomorphic
more » ... nce. 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 k-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.
doi:10.1109/focs.2018.00031 dblp:conf/focs/Carbonnel0Z18 fatcat:thbmrv7vgjhubawdkeg2fxwr54