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Computing the L1 Geodesic Diameter and Center of a Polygonal Domain

Authors Sang Won Bae, Matias Korman, Joseph S. B. Mitchell, Yoshio Okamoto, Valentin Polishchuk, Haitao Wang

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Sang Won Bae
Matias Korman
Joseph S. B. Mitchell
Yoshio Okamoto
Valentin Polishchuk
Haitao Wang

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Sang Won Bae, Matias Korman, Joseph S. B. Mitchell, Yoshio Okamoto, Valentin Polishchuk, and Haitao Wang. Computing the L1 Geodesic Diameter and Center of a Polygonal Domain. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.STACS.2016.14

Abstract

For a polygonal domain with h holes and a total of n vertices, we present algorithms that compute the L_1 geodesic diameter in O(n^2+h^4) time and the L_1 geodesic center in O((n^4+n^2 h^4)*alpha(n)) time, where alpha(.) 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(n^{7.73}) or O(n^7(h+log(n))) time, and compute the geodesic center in O(n^{12+epsilon}) time. Therefore, our algorithms are much faster than the algorithms for the Euclidean problems. Our algorithms are based on several interesting observations on L_1 shortest paths in polygonal domains.
Keywords
  • geodesic diameter
  • geodesic center
  • shortest paths
  • polygonal domains
  • L1 metric

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