License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2016.14
URN: urn:nbn:de:0030-drops-57151
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5715/
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Won Bae, Sang ; Korman, Matias ; Mitchell, Joseph S. B. ; Okamoto, Yoshio ; Polishchuk, Valentin ; Wang, Haitao

Computing the L1 Geodesic Diameter and Center of a Polygonal Domain

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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.

BibTeX - Entry

@InProceedings{wonbae_et_al:LIPIcs:2016:5715,
  author =	{Sang Won Bae and Matias Korman and Joseph S. B. Mitchell and Yoshio Okamoto and Valentin Polishchuk and Haitao Wang},
  title =	{{Computing the L1 Geodesic Diameter and Center of a Polygonal Domain}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5715},
  URN =		{urn:nbn:de:0030-drops-57151},
  doi =		{10.4230/LIPIcs.STACS.2016.14},
  annote =	{Keywords: geodesic diameter, geodesic center, shortest paths, polygonal domains, L1 metric}
}

Keywords: geodesic diameter, geodesic center, shortest paths, polygonal domains, L1 metric
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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