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arXiv · 2308.15635

Parameterized and Approximation Algorithms for the Maximum Bimodal Subgraph Problem

Walter Didimo·Fedor V. Fomin·Petr A. Golovach·Tanmay Inamdar·Stephen Kobourov·Marie Diana Sieper
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Abstract

A vertex of a plane digraph is bimodal if all its incoming edges (and hence all its outgoing edges) are consecutive in the cyclic order around it. A plane digraph is bimodal if all its vertices are bimodal. Bimodality is at the heart of many types of graph layouts, such as upward drawings, level-planar drawings, and L-drawings. If the graph is not bimodal, the Maximum Bimodal Subgraph (MBS) problem asks for an embedding-preserving bimodal subgraph with the maximum number of edges. We initiate the study of the MBS problem from the parameterized complexity perspective with two main results: (i) we describe an FPT algorithm parameterized by the branchwidth (and hence by the treewidth) of the graph; (ii) we establish that MBS parameterized by the number of non-bimodal vertices admits a polynomial kernel. As the byproduct of these results, we obtain a subexponential FPT algorithm and an efficient polynomial-time approximation scheme for MBS.

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Walter Didimo, Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Stephen Kobourov, Marie Diana Sieper. 2023-08-29. Parameterized and Approximation Algorithms for the Maximum Bimodal Subgraph Problem. https://arxiv.org/abs/2308.15635

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