Contracting a planar graph efficiently

Jacob Holm, Giuseppe F. Italiano, Adam Karczmarz, Jakub Łacki, Eva Rotenberg, Piotr Sankowski

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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.

Original languageEnglish
Title of host publication25th European Symposium on Algorithms, ESA 2017
Volume87
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication date1 Sep 2017
Article number50
ISBN (Electronic)9783959770491
DOIs
Publication statusPublished - 1 Sep 2017
Event25th European Symposium on Algorithms (ESA 2017) - Vienna, Austria
Duration: 4 Sep 20176 Sep 2017

Conference

Conference25th European Symposium on Algorithms (ESA 2017)
CountryAustria
CityVienna
Period04/09/201706/09/2017

Keywords

  • Algorithms
  • Coloring
  • Connectivity
  • Data structures
  • Planar graphs

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