Exploring the complexity of layout parameters in tournaments and
semi-complete digraphs
release_7aoy6ah4znbbzc6u77xckl2hwe
by
Florian Barbero, Christophe Paul, Michał Pilipczuk
2017
Abstract
A simple digraph is semi-complete if for any two of its vertices u and v,
at least one of the arcs (u,v) and (v,u) is present. We study the
complexity of computing two layout parameters of semi-complete digraphs:
cutwidth and optimal linear arrangement (OLA). We prove that: (1) Both
parameters are NP-hard to compute and the known exact and
parameterized algorithms for them have essentially optimal running times,
assuming the Exponential Time Hypothesis; (2) The cutwidth parameter admits a
quadratic Turing kernel, whereas it does not admit any polynomial kernel unless
NP⊆coNP/poly. By contrast, OLA admits a
linear kernel. These results essentially complete the complexity analysis of
computing cutwidth and OLA on semi-complete digraphs. Our techniques can be
also used to analyze the sizes of minimal obstructions for having small
cutwidth under the induced subdigraph relation.
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