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.

• Type: Conference
• Year: 2003
• Where: FOCS
• Authors: Martin Grohe
• Keywords: Complexity Theoretic Assumption, Complexity Theoretic Classification, Constraint Satisfaction Problems, FOCS 2003, Theoretical Computer Science