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.ISAAC.2017.61
URN: urn:nbn:de:0030-drops-82401
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8240/
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Oh, Eunjin ; Ahn, Hee-Kap

A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-off Algorithms

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LIPIcs-ISAAC-2017-61.pdf (0.6 MB)

Abstract

We are given a read-only memory for input and a write-only stream for output. For a positive integer parameter s, an s-workspace algorithm is an algorithm using only O(s) words of workspace in addition to the memory for input. In this paper, we present an O(n^2/s)-time s-workspace algorithm for subdividing a simple polygon into O(\min\{n/s,s\}) subpolygons of complexity O(\max\{n/s,s\}).

As applications of the subdivision, the previously best known time-space trade-offs for the following three geometric problems are improved immediately: (1) computing the shortest path between two points inside a simple n-gon, (2) computing the shortest path tree from a point inside a simple n-gon, (3) computing a triangulation of a simple n-gon. In addition, we improve the algorithm for the second problem even further.

BibTeX - Entry

@InProceedings{oh_et_al:LIPIcs:2017:8240,
  author =	{Eunjin Oh and Hee-Kap Ahn},
  title =	{{A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-off Algorithms}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{61:1--61:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Yoshio Okamoto and Takeshi Tokuyama},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8240},
  URN =		{urn:nbn:de:0030-drops-82401},
  doi =		{10.4230/LIPIcs.ISAAC.2017.61},
  annote =	{Keywords: Time-space trade-off, simple polygon, shortest path, shortest path tree}
}

Keywords: Time-space trade-off, simple polygon, shortest path, shortest path tree
Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 07.12.2017

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