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Type: Artigo
Title: Polynomial-time Approximation Schemes For Circle And Other Packing Problems
Author: Miyazawa
Flavio K.; Pedrosa
Lehilton L. C.; Schouery
Rafael C. S.; Sviridenko
Maxim; Wakabayashi
Abstract: We consider the problem of packing a set of circles into a minimum number of unit square bins. To obtain rational solutions, we use augmented bins of height , for some arbitrarily small number . For this problem, we obtain an asymptotic approximation scheme (APTAS) that is polynomial on , and thus may be given as part of the problem input. For the special case that is constant, we give a (one dimensional) resource augmentation scheme, that is, we obtain a packing into bins of unit width and height using no more than the number of bins in an optimal packing without resource augmentation. Additionally, we obtain an APTAS for the circle strip packing problem, whose goal is to pack a set of circles into a strip of unit width and minimum height. Our algorithms are the first approximation schemes for circle packing problems, and are based on novel ideas of iteratively separating small and large items, and may be extended to a wide range of packing problems that satisfy certain conditions. These extensions comprise problems with different kinds of items, such as regular polygons, or with bins of different shapes, such as circles and spheres. As an example, we obtain APTAS's for the problems of packing d-dimensional spheres into hypercubes under the L-p-norm.
Subject: Circle Bin Packing
Circle Strip Packing
Asymptotic Approximation Scheme
Resource Augmentation Scheme
Sphere Packing
Algebraic Algorithms
Editor: Springer
New York
Rights: fechado
Identifier DOI: 10.1007/s00453-015-0052-4
Date Issue: 2016
Appears in Collections:Unicamp - Artigos e Outros Documentos

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