The complexity of general-valued CSPs seen from the other side

Clement Carbonnel; Miguel Romero; Stanislav Zivny

doi:10.1137/19m1250121

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arXiv · 1710.03148

The complexity of general-valued CSPs seen from the other side

Clement Carbonnel·Miguel Romero·Stanislav Zivny

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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 $k$-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.

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Clement Carbonnel, Miguel Romero, Stanislav Zivny. 2017-10-09. The complexity of general-valued CSPs seen from the other side. https://doi.org/10.1137/19m1250121

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