Journal ArticleDOI
The complexity of homomorphism and constraint satisfaction problems seen from the other side
TLDR
It is proved that, under some complexity theoretic assumption from parameterized complexity theory, HOM(C,−) is in polynomial time if and only if C has bounded tree width modulo homomorphic equivalence.Abstract:
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 s. 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 tree width 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.read more
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Analysis of Boolean Functions
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Proceedings ArticleDOI
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References
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Foundations of databases
TL;DR: This book discusses Languages, Computability, and Complexity, and the Relational Model, which aims to clarify the role of Semantic Data Models in the development of Query Language Design.
Book
Parameterized Complexity
TL;DR: An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability, and introduces readers to new classes of algorithms which may be analysed more precisely than was the case until now.
Book
Parameterized complexity theory
Jörg Flum,Martin Grohe +1 more
TL;DR: Fixed-Parameter Tractability.
Proceedings ArticleDOI
The complexity of satisfiability problems
TL;DR: An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.
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