Ordinal Embedding Relaxations Parameterized Above Tight Lower Bound

Details Ordinal Embedding Relaxations Parameterized Above Tight Lower Bound Ordinal Embedding Relaxations Parameterized Above Tight Lower Bound

2009-07-30

arxiv.org/abs/0907.5427v2

Computer Science

Data Structures and Algorithms

Scientific paper

We study ordinal embedding relaxations in the realm of parameterized complexity. We prove the existence of a quadratic kernel for the {\sc Betweenness} problem parameterized above tight lower bound, which is stated as follows. For a set $V$ of variables and set $\mathcal C$ of constraints "$v_i$ {is between} $v_j$ {and} $v_k$", decide whether there is a bijection from $V$ to the set $\{1,...,|V|\}$ satisfying at least $|\mathcal C|/3 + \kappa$ of the constraints in $\mathcal C$. Our result solves an open problem attributed to Benny Chor in Niedermeier's monograph "Invitation to Fixed-Parameter Algorithms". 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.

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