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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.128
URN: urn:nbn:de:0030-drops-46938
URL: https://drops.dagstuhl.de/opus/volltexte/2014/4693/
Dumitrescu, Adrian ; Jiang, Minghui ; Tóth, Csaba D.
Computing Opaque Interior Barriers à la Shermer
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Abstract
The problem of finding a collection of curves of minimum total length that meet all the lines intersecting a given polygon was initiated byMazurkiewicz in 1916. Such a collection forms an opaque barrier for the polygon. In 1991 Shermer proposed an exponential-time algorithm that computes an interior-restricted barrier made of segments for any given convex n-gon. He conjectured that the barrier found by his algorithm is optimal, however this was refuted recently by Provan et al. Here we give a Shermer like algorithm that computes an interior polygonal barrier whose length is at most 1.7168 times the optimal and that runs in O(n) time. As a byproduct, we also deduce upper and lower bounds on the approximation ratio of Shermer's algorithm.
BibTeX - Entry
@InProceedings{dumitrescu_et_al:LIPIcs:2014:4693,
author = {Adrian Dumitrescu and Minghui Jiang and Csaba D. T{\'o}th},
title = {{Computing Opaque Interior Barriers {\`a} la Shermer}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
pages = {128--143},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-74-3},
ISSN = {1868-8969},
year = {2014},
volume = {28},
editor = {Klaus Jansen and Jos{\'e} D. P. Rolim and Nikhil R. Devanur and Cristopher Moore},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2014/4693},
URN = {urn:nbn:de:0030-drops-46938},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2014.128},
annote = {Keywords: Opaque barrier, approximation algorithm, isoperimetric inequality}
}
| Keywords: | Opaque barrier, approximation algorithm, isoperimetric inequality | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014) | |
| Issue date: | 2014 | |
| Date of publication: | 04.09.2014 |
