Subexponential-time and FPT algorithms for embedded flat clustered planarity

Giordano Da Lozzo, David Eppstein, Michael T. Goodrich, Siddharth Gupta

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations

Abstract

The C-Planarity problem asks for a drawing of a clustered graph, i.e., a graph whose vertices belong to properly nested clusters, in which each cluster is represented by a simple closed region with no edge-edge crossings, no region-region crossings, and no unnecessary edge-region crossings. We study C-Planarity for embedded flat clustered graphs, graphs with a fixed combinatorial embedding whose clusters partition the vertex set. Our main result is a subexponential-time algorithm to test C-Planarity for these graphs when their face size is bounded. Furthermore, we consider a variation of the notion of embedded tree decomposition in which, for each face, including the outer face, there is a bag that contains every vertex of the face. We show that C-Planarity is fixed-parameter tractable with the embedded-width of the underlying graph and the number of disconnected clusters as parameters.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 44th International Workshop, WG 2018, Proceedings
EditorsAndreas Brandstädt, Ekkehard Köhler, Klaus Meer
PublisherSpringer Verlag
Pages111-124
Number of pages14
ISBN (Print)9783030002558
DOIs
StatePublished - 1 Jan 2018
Externally publishedYes
Event44th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2018 - Cottbus, Germany
Duration: 27 Jun 201829 Jun 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11159 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference44th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2018
Country/TerritoryGermany
CityCottbus
Period27/06/1829/06/18

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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