Parameterized and Approximation Algorithms for the Maximum Bimodal Subgraph Problem
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.
Cite
@article{arxiv.2308.15635,
title = {Parameterized and Approximation Algorithms for the Maximum Bimodal Subgraph Problem},
author = {Walter Didimo and Fedor V. Fomin and Petr A. Golovach and Tanmay Inamdar and Stephen Kobourov and Marie Diana Sieper},
journal= {arXiv preprint arXiv:2308.15635},
year = {2023}
}
Comments
Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023)