Using the Metro-Map Metaphor for Drawing Hypergraphs

Fabian Frank, Michael Kaufmann, Stephen Kobourov, Tamara Mchedlidze, Sergey Pupyrev, Torsten Ueckerdt, Alexander Wolff

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

For a planar graph G and a set Π of simple paths in G, we define a metro-map embedding to be a planar embedding of G and an ordering of the paths of Π along each edge of G. This definition of a metro-map embedding is motivated by visual representations of hypergraphs using the metro-map metaphor. In a metro-map embedding, two paths cross in a so-called vertex crossing if they pass through the vertex and alternate in the circular ordering around it. We study the problem of constructing metro-map embeddings with the minimum number of crossing vertices, that is, vertices where paths cross. We show that the corresponding decision problem is NP-complete for general planar graphs but can be solved efficiently for trees or if the number of crossing vertices is constant. All our results hold both in a fixed and variable embedding settings.

Original languageEnglish (US)
Title of host publicationSOFSEM 2021
Subtitle of host publicationTheory and Practice of Computer Science - 47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021, Proceedings
EditorsTomáš Bureš, Riccardo Dondi, Johann Gamper, Giovanna Guerrini, Tomasz Jurdzinski, Claus Pahl, Florian Sikora, Prudence W. Wong
PublisherSpringer Science and Business Media Deutschland GmbH
Pages361-372
Number of pages12
ISBN (Print)9783030677305
DOIs
StatePublished - 2021
Event47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021 - Bolzano-Bozen, Italy
Duration: Jan 25 2021Jan 29 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12607 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021
Country/TerritoryItaly
CityBolzano-Bozen
Period1/25/211/29/21

Keywords

  • Clustered planarity
  • Crossing minimization
  • Hypergraph visualization
  • Metro-map metaphor
  • NP-hardness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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