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FOCS

2003

IEEE

2003

IEEE

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.

Related Content

Added |
04 Jul 2010 |

Updated |
04 Jul 2010 |

Type |
Conference |

Year |
2003 |

Where |
FOCS |

Authors |
Martin Grohe |

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