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Polynomial-Time Approximation Schemes for Packing and Piercing Fat Objects (2001)
| Venue: | JOURNAL OF ALGORITHMS |
| Citations: | 50 - 5 self |
BibTeX
@ARTICLE{Chan01polynomial-timeapproximation,
author = {Timothy M. Chan},
title = {Polynomial-Time Approximation Schemes for Packing and Piercing Fat Objects},
journal = {JOURNAL OF ALGORITHMS},
year = {2001},
volume = {46},
pages = {178--189}
}
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Abstract
We consider two problems: given a collection of n fat objects in a xed dimension, 1. (packing) nd the maximum subcollection of pairwise disjoint objects, and 2. (piercing) nd the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomial-time approximation scheme (PTAS) for the packing problem, based on a shifted hierarchical subdivision method. Using shifted quadtrees, we describe a similar algorithm for packing but with a smaller time bound. Erlebach et al.'s algorithm requires polynomial space. We describe a dierent algorithm, based on geometric separators, that requires only linear space. This algorithm can also be applied to piercing, yielding the rst PTAS for that problem. Abbreviated title. Packing and Piercing Fat Objects.
Keyphrases
polynomial-time approximation scheme piercing fat object fat object packing problem polynomial space dierent algorithm time bound maximum subcollection rst ptas computational geometry geometric separator xed dimension maximum independent set shifted quadtrees abbreviated title linear space shifted hierarchical subdivision method approximation algorithm similar algorithm dynamic programming separator theorem minimum point pairwise disjoint object
