Abstract:We study ordinal embedding relaxations in the realm of parameterized complexity. We prove the existence of a quadratic kernel for the Betweenness problem parameterized above tight lower bound, which i...We study ordinal embedding relaxations in the realm of parameterized complexity. We prove the existence of a quadratic kernel for the Betweenness problem parameterized above tight lower bound, which is stated as follows. For a set V of variables and set C of constraints \vi is between vj and vk, decide whether there is a bijection from V to the set f1;:::;jV jg satisfying at least jCj=3+• of the constraints in C. Our result solves an open problem attributed to Benny Chor in Niedermeier’s monograph \Invitation to Fixed-Parameter Algorithms. The betweenness problem is of interest in molecular biology. An approach developed in this paper can be used to determine parameterized complexity of a number of other optimization problems on permutations parameterized above or below tight bounds.Read More
Publication Year: 2009
Publication Date: 2009-07-30
Language: en
Type: article
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Cited By Count: 10
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