Orthogonal layout with optimal face complexity

M. Jawaherul Alam, Stephen G. Kobourov, Debajyoti Mondal

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

3 Scopus citations

Abstract

We study a problem motivated by rectilinear schematization of geographic maps. Given a biconnected plane graph G and an integer k ≥ 0, does G have a strict-orthogonal drawing with at most k reflex angles per face? For k = 0 the problem is equivalent to realizing each face as a rectangle. The problem can be reduced to a max-flow problem in some linear-size nonplanar network, but the best solutions require Ω(n1.5 log n log k) time. We describe a graph matching approach that can decide strict-orthogonal drawability for arbitrary reflex complexity k in O((nk)1.5) time, which is faster for constant values of k. In contrast, if the embedding is not fixed, we prove that it is NP-complete to decide whether a planar graph admits a strict-orthogonal drawing with reflex face complexity 4.

Original languageEnglish (US)
Title of host publicationSOFSEM 2016
Subtitle of host publicationTheory and Practice of Computer Science - 42nd International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings
EditorsRūsiņš Mārtiņš Freivalds, Gregor Engels, Barbara Catania
PublisherSpringer-Verlag
Pages121-133
Number of pages13
ISBN (Print)9783662491911
DOIs
StatePublished - 2016
Event42nd International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2016 - Harrachov, Czech Republic
Duration: Jan 23 2016Jan 28 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9587
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other42nd International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2016
CountryCzech Republic
CityHarrachov
Period1/23/161/28/16

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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