Computing the L 1 Geodesic Diameter and Center of a Simple Polygon in Linear Time

Sang Won Bae, Matias Korman, Yoshio Okamoto, Haitao Wang

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

3 Citations (Scopus)

Abstract

In this paper, we show that the L 1 geodesic diameter and center of a simple polygon can be computed in linear time. For the purpose, we focus on revealing basic geometric properties of the L 1 geodesic balls, that is, the metric balls with respect to the L 1 geodesic distance. More specifically, in this paper we show that any family of L 1 geodesic balls in any simple polygon has Helly number two, and the L 1 geodesic center consists of midpoints of shortest paths between diametral pairs. These properties are crucial for our linear-time algorithms, and do not hold for the Euclidean case.

Original languageEnglish
Title of host publicationLATIN 2014
Subtitle of host publicationTheoretical Informatics - 11th Latin American Symposium, Proceedings
PublisherSpringer Verlag
Pages120-131
Number of pages12
ISBN (Print)9783642544224
DOIs
Publication statusPublished - 2014
Externally publishedYes
Event11th Latin American Theoretical Informatics Symposium, LATIN 2014 - Montevideo, Uruguay
Duration: 2014 Mar 312014 Apr 4

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8392 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th Latin American Theoretical Informatics Symposium, LATIN 2014
CountryUruguay
CityMontevideo
Period14/3/3114/4/4

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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