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DOI: 10.4230/LIPIcs.SOCG.2015.111
URN: urn:nbn:de:0030-drops-50941
URL: https://drops.dagstuhl.de/opus/volltexte/2015/5094/
Har-Peled, Sariel
Shortest Path in a Polygon using Sublinear Space
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Abstract
We resolve an open problem due to Tetsuo Asano, showing how to compute the shortest path in a polygon, given in a read only memory, using sublinear space and subquadratic time. Specifically, given a simple polygon P with n vertices in a read only memory, and additional working memory of size m, the new algorithm computes the shortest path (in P) in O(n^2 / m) expected time, assuming m = O(n / log^2 n). This requires several new tools, which we believe to be of independent interest. Specifically, we show that violator space problems, an abstraction of low dimensional linear-programming (and LP-type problems), can be solved using constant space and expected linear time, by modifying Seidel's linear programming algorithm and using pseudo-random sequences.
BibTeX - Entry
@InProceedings{harpeled:LIPIcs:2015:5094,
author = {Sariel Har-Peled},
title = {{Shortest Path in a Polygon using Sublinear Space}},
booktitle = {31st International Symposium on Computational Geometry (SoCG 2015)},
pages = {111--125},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-83-5},
ISSN = {1868-8969},
year = {2015},
volume = {34},
editor = {Lars Arge and J{\'a}nos Pach},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5094},
URN = {urn:nbn:de:0030-drops-50941},
doi = {10.4230/LIPIcs.SOCG.2015.111},
annote = {Keywords: Shortest path, violator spaces, limited space}
}
| Keywords: | Shortest path, violator spaces, limited space | |
| Seminar: | 31st International Symposium on Computational Geometry (SoCG 2015) | |
| Issue date: | 2015 | |
| Date of publication: | 12.06.2015 |
