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.SWAT.2018.5
URN: urn:nbn:de:0030-drops-88312
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8831/
Agarwal, Pankaj K. ;
Kumar, Neeraj ;
Sintos, Stavros ;
Suri, Subhash
Computing Shortest Paths in the Plane with Removable Obstacles
Abstract
We consider the problem of computing a Euclidean shortest path in the presence of removable obstacles in the plane. In particular, we have a collection of pairwise-disjoint polygonal obstacles, each of which may be removed at some cost c_i > 0. Given a cost budget C > 0, and a pair of points s, t, which obstacles should be removed to minimize the path length from s to t in the remaining workspace? We show that this problem is NP-hard even if the obstacles are vertical line segments. Our main result is a fully-polynomial time approximation scheme (FPTAS) for the case of convex polygons. Specifically, we compute an (1 + epsilon)-approximate shortest path in time O({nh}/{epsilon^2} log n log n/epsilon) with removal cost at most (1+epsilon)C, where h is the number of obstacles, n is the total number of obstacle vertices, and epsilon in (0, 1) is a user-specified parameter. Our approximation scheme also solves a shortest path problem for a stochastic model of obstacles, where each obstacle's presence is an independent event with a known probability. Finally, we also present a data structure that can answer s-t path queries in polylogarithmic time, for any pair of points s, t in the plane.
BibTeX - Entry
@InProceedings{agarwal_et_al:LIPIcs:2018:8831,
author = {Pankaj K. Agarwal and Neeraj Kumar and Stavros Sintos and Subhash Suri},
title = {{Computing Shortest Paths in the Plane with Removable Obstacles}},
booktitle = {16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
pages = {5:1--5:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-068-2},
ISSN = {1868-8969},
year = {2018},
volume = {101},
editor = {David Eppstein},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8831},
URN = {urn:nbn:de:0030-drops-88312},
doi = {10.4230/LIPIcs.SWAT.2018.5},
annote = {Keywords: Euclidean shortest paths, Removable polygonal obstacles, Stochastic shortest paths, L_1 shortest paths}
}
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Keywords: |
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Euclidean shortest paths, Removable polygonal obstacles, Stochastic shortest paths, L_1 shortest paths |
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Collection: |
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16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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04.06.2018 |
