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Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain

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

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Author Details

Elena Arseneva
  • St. Petersburg State University, St. Petersburg, Russia
Man-Kwun Chiu
  • Institut für Informatik, Freie Universität Berlin, Berlin, Germany
Matias Korman
  • Tufts University, Boston, USA
Aleksandar Markovic
  • TU Eindhoven, Eindhoven, The Netherlands
Yoshio Okamoto
  • University of Electro-Communications, Tokyo, Japan, RIKEN Center for Advanced Intelligent Project, Tokyo, Japan
Aurélien Ooms
  • Université libre de Bruxelles (ULB), Brussels, Belgium
André van Renssen
  • University of Sydney, Sydney, Australia
Marcel Roeloffzen
  • TU Eindhoven, Eindhoven, The Netherlands

Funding

  • Arseneva, Elena: Partially supported by the SNF Early Postdoc Mobility grant P2TIP2-168563, Switzerland, and F.R.S.-FNRS, Belgium.
  • Chiu, Man-Kwun: Supported in part by ERC StG 757609.
  • Korman, Matias: Supported in part by KAKENHI No. 17K12635, Japan and NSF award CCF-1422311.
  • Markovic, Aleksandar: Supported by the Netherlands' Organisation for Scientific Research (NWO) under project no. 024.002.003.
  • Okamoto, Yoshio: Partially supported by JSPS KAKENHI Grant Number 15K00009 and JST CREST Grant Number JPMJCR1402, and Kayamori Foundation of Informational Science Advancement.
  • Ooms, Aurélien: Supported by the Fund for Research Training in Industry and Agriculture (FRIA).
  • van Renssen, André: Supported by JST ERATO Grant Number JPMJER1201, Japan.

Cite As Get BibTex

Elena Arseneva, Man-Kwun Chiu, Matias Korman, Aleksandar Markovic, Yoshio Okamoto, Aurélien Ooms, André van Renssen, and Marcel Roeloffzen. Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 58:1-58:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ISAAC.2018.58

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(n^omega, n^2 + nh log h + chi^2)) time, where omega<2.373 denotes the matrix multiplication exponent and chi in Omega(n) cap O(n^2) 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(n^2 log n) time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Rectilinear link distance
  • polygonal domain
  • diameter
  • radius

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References

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