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.SoCG.2017.60
URN: urn:nbn:de:0030-drops-71876
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7187/
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Wang, Haitao

Bicriteria Rectilinear Shortest Paths among Rectilinear Obstacles in the Plane

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LIPIcs-SoCG-2017-60.pdf (0.6 MB)

Abstract

Given a rectilinear domain P of h pairwise-disjoint rectilinear obstacles with a total of n vertices in the plane, we study the problem of computing bicriteria rectilinear shortest paths between two points s and t in P. Three types of bicriteria rectilinear paths are considered: minimum-link shortest paths, shortest minimum-link paths, and minimum-cost paths where the cost of a path is a non-decreasing function of both the number of edges and the length of the path. The one-point and two-point path queries are also considered. Algorithms for these problems have been given previously. Our contributions are threefold. First, we find a critical error in all previous algorithms. Second, we correct the error in a not-so-trivial way. Third, we further improve the algorithms so that they are even faster than the previous (incorrect) algorithms when h is relatively small. For example, for computing a minimum-link shortest s-t path, the previous algorithm runs in O(n log^{3/2} n) time while the time of our new algorithm is O(n + h log^{3/2} h).

BibTeX - Entry

@InProceedings{wang:LIPIcs:2017:7187,
  author =	{Haitao Wang},
  title =	{{Bicriteria Rectilinear Shortest Paths among Rectilinear Obstacles in the Plane}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{60:1--60:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7187},
  URN =		{urn:nbn:de:0030-drops-71876},
  doi =		{10.4230/LIPIcs.SoCG.2017.60},
  annote =	{Keywords: rectilinear paths, shortest paths, minimum-link paths, bicriteria paths, rectilinear polygons}
}

Keywords: rectilinear paths, shortest paths, minimum-link paths, bicriteria paths, rectilinear polygons
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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