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arXiv · 1507.01688

A Fixed Parameter Tractable Approximation Scheme for the Optimal Cut Graph of a Surface

Vincent Cohen-Addad·Arnaud de Mesmay
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Abstract

Given a graph $G$ cellularly embedded on a surface $\Sigma$ of genus $g$, a cut graph is a subgraph of $G$ such that cutting $\Sigma$ along $G$ yields a topological disk. We provide a fixed parameter tractable approximation scheme for the problem of computing the shortest cut graph, that is, for any $\varepsilon >0$, we show how to compute a $(1+ \varepsilon)$ approximation of the shortest cut graph in time $f(\varepsilon, g)n^3$. Our techniques first rely on the computation of a spanner for the problem using the technique of brick decompositions, to reduce the problem to the case of bounded tree-width. Then, to solve the bounded tree-width case, we introduce a variant of the surface-cut decomposition of Ru\'e, Sau and Thilikos, which may be of independent interest.

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Vincent Cohen-Addad, Arnaud de Mesmay. 2015-07-07. A Fixed Parameter Tractable Approximation Scheme for the Optimal Cut Graph of a Surface. https://arxiv.org/abs/1507.01688

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