The Geodesic Diameter of Polygonal Domains

Sang Won Bae, Matias Korman, Yoshio Okamoto

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

This paper studies the geodesic diameter of polygonal domains having h holes and n corners. For simple polygons (i.e., h = 0), the geodesic diameter is determined by a pair of corners of a given polygon and can be computed in linear time, as shown by Hershberger and Suri. For general polygonal domains with h ≥ 1, however, no algorithm for computing the geodesic diameter was known prior to this paper. In this paper, we present the first algorithms that compute the geodesic diameter of a given polygonal domain in worst-case time O(n7.73) or O(n7(log n + h)). The main difficulty unlike the simple polygon case relies on the following observation revealed in this paper: two interior points can determine the geodesic diameter and in that case there exist at least five distinct shortest paths between the two.

Original languageEnglish
Pages (from-to)306-329
Number of pages24
JournalDiscrete and Computational Geometry
Volume50
Issue number2
DOIs
Publication statusPublished - 2013 Sep 1
Externally publishedYes

Keywords

  • Convex function
  • Exact algorithm
  • Geodesic diameter
  • Lower envelope
  • Polygonal domain
  • Shortest path

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Fingerprint Dive into the research topics of 'The Geodesic Diameter of Polygonal Domains'. Together they form a unique fingerprint.

  • Cite this