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VigneronAntoine

Vigneron, Antoine
Geometric Algorithms Lab.
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Geometric Optimization and Sums of Algebraic Functions

Author(s)
Vigneron, Antoine
Issued Date
2014-01
DOI
10.1145/2532647
URI
https://scholarworks.unist.ac.kr/handle/201301/19644
Fulltext
http://dl.acm.org/citation.cfm?doid=2578701.2532647
Citation
ACM TRANSACTIONS ON ALGORITHMS, v.10, no.1, pp.4
Abstract
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls
Publisher
ASSOC COMPUTING MACHINERY
ISSN
1549-6325

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