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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

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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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