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FOCS
2003
IEEE

The Complexity of Homomorphism and Constraint Satisfaction Problems Seen from the Other Side

14 years 3 months ago
The Complexity of Homomorphism and Constraint Satisfaction Problems Seen from the Other Side
We give a complexity theoretic classification of homomorphism problems for graphs and, more generally, relational structures obtained by restricting the left hand side structure in a homomorphism. For every class C of structures, let HOM(C, −) be the problem of deciding whether a given structure A ∈ C has a homomorphism to a given (arbitrary) structure B. We prove that, under some complexity theoretic assumption from parameterized complexity theory, HOM(C, −) is in polynomial time if and only if C has bounded treewidth modulo homomorphic equivalence. Translated into the language of constraint satisfaction problems, our result yields a characterization of the tractable structural restrictions of constraint satisfaction problems. Translated into the language of database theory, it implies a characterization of the tractable instances of the evaluation problem for conjunctive queries over relational databases.
Martin Grohe
Added 04 Jul 2010
Updated 04 Jul 2010
Type Conference
Year 2003
Where FOCS
Authors Martin Grohe
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