License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.53
URN: urn:nbn:de:0030-drops-87663
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8766/
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Klute, Fabian ; Nöllenburg, Martin

Minimizing Crossings in Constrained Two-Sided Circular Graph Layouts

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LIPIcs-SoCG-2018-53.pdf (0.6 MB)

Abstract

Circular layouts are a popular graph drawing style, where vertices are placed on a circle and edges are drawn as straight chords. Crossing minimization in circular layouts is NP-hard. One way to allow for fewer crossings in practice are two-sided layouts that draw some edges as curves in the exterior of the circle. In fact, one- and two-sided circular layouts are equivalent to one-page and two-page book drawings, i.e., graph layouts with all vertices placed on a line (the spine) and edges drawn in one or two distinct half-planes (the pages) bounded by the spine. In this paper we study the problem of minimizing the crossings for a fixed cyclic vertex order by computing an optimal k-plane set of exteriorly drawn edges for k >= 1, extending the previously studied case k=0. We show that this relates to finding bounded-degree maximum-weight induced subgraphs of circle graphs, which is a graph-theoretic problem of independent interest. We show NP-hardness for arbitrary k, present an efficient algorithm for k=1, and generalize it to an explicit XP-time algorithm for any fixed k. For the practically interesting case k=1 we implemented our algorithm and present experimental results that confirm the applicability of our algorithm.

BibTeX - Entry

@InProceedings{klute_et_al:LIPIcs:2018:8766,
  author =	{Fabian Klute and Martin N{\"o}llenburg},
  title =	{{Minimizing Crossings in Constrained Two-Sided Circular Graph Layouts}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{53:1--53:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8766},
  URN =		{urn:nbn:de:0030-drops-87663},
  doi =		{10.4230/LIPIcs.SoCG.2018.53},
  annote =	{Keywords: Graph Drawing, Circular Layouts, Crossing Minimization, Circle Graphs, Bounded-Degree Maximum-Weight Induced Subgraphs}
}

Keywords: Graph Drawing, Circular Layouts, Crossing Minimization, Circle Graphs, Bounded-Degree Maximum-Weight Induced Subgraphs
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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