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arXiv · 1908.08911

Parameterized Algorithms for Book Embedding Problems

Sujoy Bhore·Robert Ganian·Fabrizio Montecchiani·Martin Nöllenburg
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Abstract

A k-page book embedding of a graph G draws the vertices of G on a line and the edges on k half-planes (called pages) bounded by this line, such that no two edges on the same page cross. We study the problem of determining whether G admits a k-page book embedding both when the linear order of the vertices is fixed, called Fixed-Order Book Thickness, or not fixed, called Book Thickness. Both problems are known to be NP-complete in general. We show that Fixed-Order Book Thickness and Book Thickness are fixed-parameter tractable parameterized by the vertex cover number of the graph and that Fixed-Order Book Thickness is fixed-parameter tractable parameterized by the pathwidth of the vertex order.

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Sujoy Bhore, Robert Ganian, Fabrizio Montecchiani, Martin Nöllenburg. 2019-08-23. Parameterized Algorithms for Book Embedding Problems. https://arxiv.org/abs/1908.08911

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