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.ESA.2017.50
URN: urn:nbn:de:0030-drops-78755
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7875/
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Holm, Jacob ; Italiano, Giuseppe F. ; Karczmarz, Adam ; Lacki, Jakub ; Rotenberg, Eva ; Sankowski, Piotr

Contracting a Planar Graph Efficiently

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LIPIcs-ESA-2017-50.pdf (0.6 MB)

Abstract

We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in O(1) time. Moreover, it can report all the arising self-loops and parallel edges.

By applying the data structure, we can achieve optimal running times for decremental bridge detection, 2-edge connectivity, maximal 3-edge connected components, and the problem of finding a unique perfect matching for a static planar graph. Furthermore, we improve the running times of algorithms for several planar graph problems, including decremental 2-vertex and 3-edge connectivity, and we show that using our data structure in a black-box manner, one obtains conceptually simple optimal algorithms for computing MST and 5-coloring in planar graphs.

BibTeX - Entry

@InProceedings{holm_et_al:LIPIcs:2017:7875,
  author =	{Jacob Holm and Giuseppe F. Italiano and Adam Karczmarz and Jakub Lacki and Eva Rotenberg and Piotr Sankowski},
  title =	{{Contracting a Planar Graph Efficiently}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Kirk Pruhs and Christian Sohler},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7875},
  URN =		{urn:nbn:de:0030-drops-78755},
  doi =		{10.4230/LIPIcs.ESA.2017.50},
  annote =	{Keywords: planar graphs, algorithms, data structures, connectivity, coloring}
}

Keywords: planar graphs, algorithms, data structures, connectivity, coloring
Collection: 25th Annual European Symposium on Algorithms (ESA 2017)
Issue Date: 2017
Date of publication: 01.09.2017

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