Dynamic planar embeddings of dynamic graphs

Jacob Holm, Eva Rotenberg

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

Abstract

We present an algorithm to support the dynamic embedding in the plane of a dynamic graph. An edge can be inserted across a face between two vertices on the boundary (we call such a vertex pair linkable), and edges can be deleted. The planar embedding can also be changed locally by flipping components that are connected to the rest of the graph by at most two vertices. Given vertices u, v, linkable(u, v) decides whether u and v are linkable, and if so, returns a list of suggestions for the placement of (u, v) in the embedding. For non-linkable vertices u, v, we define a new query, one-flip-linkable(u, v) providing a suggestion for a flip that will make them linkable if one exists. We will support all updates and queries in O(log2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph. Our new algorithm is simpler, exploiting that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common Euler tour.

Original languageEnglish
Title of host publication32nd International Symposium on Theoretical Aspects of Computer Science, STACS 2015
Number of pages13
Volume30
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publication date1 Feb 2015
Pages434-446
ISBN (Electronic)9783939897781
DOIs
Publication statusPublished - 1 Feb 2015
Event32nd International Symposium on Theoretical Aspects of Computer Science, STACS 2015 - Garching, Germany
Duration: 4 Mar 20157 Mar 2015

Conference

Conference32nd International Symposium on Theoretical Aspects of Computer Science, STACS 2015
CountryGermany
CityGarching
Period04/03/201507/03/2015

Keywords

  • Data structures
  • Dynamic graphs
  • Planar embeddings

Cite this

Holm, J., & Rotenberg, E. (2015). Dynamic planar embeddings of dynamic graphs. In 32nd International Symposium on Theoretical Aspects of Computer Science, STACS 2015 (Vol. 30, pp. 434-446). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.STACS.2015.434