Computing the L1 geodesic diameter and center of a simple polygon in linear time

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

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

In this paper, we show that the L1 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 L1 geodesic balls, that is, the metric balls with respect to the L1 geodesic distance. More specifically, in this paper we show that any family of L1 geodesic balls in any simple polygon has Helly number two, and the L1 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
Pages (from-to)495-505
Number of pages11
JournalComputational Geometry: Theory and Applications
Volume48
Issue number6
DOIs
Publication statusPublished - 2015 Aug
Externally publishedYes

Keywords

  • Geodesic center
  • Geodesic diameter
  • L1 metric
  • Simple polygon

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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