Computing the L1 geodesic diameter and center of a polygonal domain

Sang Won Bae, Matias Korman, Joseph S.B. Mitchell, Yoshio Okamoto, Valentin Polishchuk, Haitao Wang

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

Abstract

For a polygonal domain with h holes and a total of n vertices, we present algorithms that compute the L1 geodesic diameter in O(n2+h4) time and the L1 geodesic center in O((n4+n2h4)α(n)) time, where α(·) denotes the inverse Ackermann function. No algorithms were known for these problems before. For the Euclidean counterpart, the best algorithms compute the geodesic diameter in O(n7.73) or O(n7(h+log n)) time, and compute the geodesic center in O(n12+∈) time. Therefore, our algorithms are much faster than the algorithms for the Euclidean problems. Our algorithms are based on several interesting observations on L1 shortest paths in polygonal domains.

Original languageEnglish
Title of host publication33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016
EditorsHeribert Vollmer, Nicolas Ollinger
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770019
DOIs
Publication statusPublished - 2016 Feb 1
Event33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016 - Orleans, France
Duration: 2016 Feb 172016 Feb 20

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume47
ISSN (Print)1868-8969

Other

Other33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016
CountryFrance
CityOrleans
Period16/2/1716/2/20

Keywords

  • Geodesic center
  • Geodesic diameter
  • L metric
  • Polygonal domains
  • Shortest paths

ASJC Scopus subject areas

  • Software

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