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DOI: 10.4230/LIPIcs.ISAAC.2018.39
URN: urn:nbn:de:0030-drops-99871
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9987/
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Di Giacomo, Emilio ; Eades, Peter ; Liotta, Giuseppe ; Meijer, Henk ; Montecchiani, Fabrizio

Polyline Drawings with Topological Constraints

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LIPIcs-ISAAC-2018-39.pdf (0.6 MB)


Abstract

Let G be a simple topological graph and let Gamma be a polyline drawing of G. We say that Gamma partially preserves the topology of G if it has the same external boundary, the same rotation system, and the same set of crossings as G. Drawing Gamma fully preserves the topology of G if the planarization of G and the planarization of Gamma have the same planar embedding. We show that if the set of crossing-free edges of G forms a connected spanning subgraph, then G admits a polyline drawing that partially preserves its topology and that has curve complexity at most three (i.e., at most three bends per edge). If, however, the set of crossing-free edges of G is not a connected spanning subgraph, the curve complexity may be Omega(sqrt{n}). Concerning drawings that fully preserve the topology, we show that if G has skewness k, it admits one such drawing with curve complexity at most 2k; for skewness-1 graphs, the curve complexity can be reduced to one, which is a tight bound. We also consider optimal 2-plane graphs and discuss trade-offs between curve complexity and crossing angle resolution of drawings that fully preserve the topology.

BibTeX - Entry

@InProceedings{digiacomo_et_al:LIPIcs:2018:9987,
  author =	{Emilio Di Giacomo and Peter Eades and Giuseppe Liotta and Henk Meijer and Fabrizio Montecchiani},
  title =	{{Polyline Drawings with Topological Constraints}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{39:1--39:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9987},
  URN =		{urn:nbn:de:0030-drops-99871},
  doi =		{10.4230/LIPIcs.ISAAC.2018.39},
  annote =	{Keywords: Topological graphs, graph drawing, curve complexity, skewness-k graphs, k-planar graphs}
}

Keywords: Topological graphs, graph drawing, curve complexity, skewness-k graphs, k-planar graphs
Seminar: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 27.11.2018


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