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MFCS
2007
Springer

NP by Means of Lifts and Shadows

9 years 6 months ago
NP by Means of Lifts and Shadows
We show that every NP problem is polynomially equivalent to a simple combinatorial problem: the membership problem for a special class of digraphs. These classes are defined by means of shadows (projections) and by finitely many forbidden colored (lifted) subgraphs. Our characterization is motivated by the analysis of syntactical subclasses with the full computational power of NP, which were first studied by Feder and Vardi. Our approach applies to many combinatorial problems and it induces the characterization of coloring problems (CSP) defined by means of shadows. This turns out to be related to homomorphism dualities. We prove that a class of digraphs (relational structures) defined by finitely many forbidden colored subgraphs (i.e. lifted substructures) is a CSP class if and only if all the the forbidden structures are homomorphically equivalent to trees. We show a surprising richness of coloring problems when restricted to most frequent graph classes. Using results of Neˇse...
Gábor Kun, Jaroslav Nesetril
Added 08 Jun 2010
Updated 08 Jun 2010
Type Conference
Year 2007
Where MFCS
Authors Gábor Kun, Jaroslav Nesetril
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