Rectilinear link diameter and radius in a rectilinear polygonal domain

Elena Arseneva, Man Kwun Chiu, Matias Korman, Aleksandar Markovic, Yoshio Okamoto, Aurélien Ooms, André Van Renssen, Marcel Roeloffzen

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

1 Citation (Scopus)

Abstract

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of n vertices and h holes. We introduce a graph of oriented distances to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in O(min(nω, n2 + nhlog h + χ2)) time, where ω < 2.373 denotes the matrix multiplication exponent and χ ∈ Ω(n) ∩ O(n2) is the number of edges of the graph of oriented distances. We also provide an alternative algorithm for computing the diameter that runs in O(n2 log n) time.

Original languageEnglish
Title of host publication29th International Symposium on Algorithms and Computation, ISAAC 2018
EditorsChung-Shou Liao, Wen-Lian Hsu, Der-Tsai Lee
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages58:1-58:13
ISBN (Electronic)9783959770941
DOIs
Publication statusPublished - 2018 Dec 1
Event29th International Symposium on Algorithms and Computation, ISAAC 2018 - Jiaoxi, Yilan, Taiwan, Province of China
Duration: 2018 Dec 162018 Dec 19

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume123
ISSN (Print)1868-8969

Conference

Conference29th International Symposium on Algorithms and Computation, ISAAC 2018
CountryTaiwan, Province of China
CityJiaoxi, Yilan
Period18/12/1618/12/19

Keywords

  • Diameter
  • Polygonal domain
  • Radius
  • Rectilinear link distance

ASJC Scopus subject areas

  • Software

Cite this