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.ICALP.2018.78
URN: urn:nbn:de:0030-drops-90822
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9082/
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Hayashi, Koyo

A Polynomial Time Algorithm to Compute Geodesics in CAT(0) Cubical Complexes

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LIPIcs-ICALP-2018-78.pdf (0.7 MB)

Abstract

This paper presents the first polynomial time algorithm to compute geodesics in a CAT(0) cubical complex in general dimension. The algorithm is a simple iterative method to update breakpoints of a path joining two points using Miller, Owen and Provan's algorithm (Adv. in Appl. Math, 2015) as a subroutine. Our algorithm is applicable to any CAT(0) space in which geodesics between two close points can be computed, not limited to CAT(0) cubical complexes.

BibTeX - Entry

@InProceedings{hayashi:LIPIcs:2018:9082,
  author =	{Koyo Hayashi},
  title =	{{A Polynomial Time Algorithm to Compute Geodesics in CAT(0) Cubical Complexes}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{78:1--78:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9082},
  URN =		{urn:nbn:de:0030-drops-90822},
  doi =		{10.4230/LIPIcs.ICALP.2018.78},
  annote =	{Keywords: Geodesic, CAT(0) Space, Cubical Complex}
}

Keywords: Geodesic, CAT(0) Space, Cubical Complex
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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