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: Contribution to journalArticle

2 Citations (Scopus)

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, respectively, 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(n11log n) time. Therefore, our algorithms are significantly 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
Pages (from-to)674-701
Number of pages28
JournalDiscrete and Computational Geometry
Volume57
Issue number3
DOIs
Publication statusPublished - 2017 Apr 1

Keywords

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

ASJC Scopus subject areas

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

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    Bae, S. W., Korman, M., Mitchell, J. S. B., Okamoto, Y., Polishchuk, V., & Wang, H. (2017). Computing the L1 Geodesic Diameter and Center of a Polygonal Domain. Discrete and Computational Geometry, 57(3), 674-701. https://doi.org/10.1007/s00454-016-9841-z