| Full text | |
| Author(s): |
Miyazawa, Flavio K.
;
Pedrosa, Lehilton L. C.
;
Schouery, Rafael C. S.
;
Sviridenko, Maxim
;
Wakabayashi, Yoshiko
Total Authors: 5
|
| Document type: | Journal article |
| Source: | ALGORITHMICA; v. 76, n. 2, p. 536-568, OCT 2016. |
| Web of Science Citations: | 5 |
| 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. (AU) | |
| FAPESP's process: | 10/20710-4 - Approximation Algorithms for Facility Location Problems with Different Distance Functions |
| Grantee: | Lehilton Lelis Chaves Pedrosa |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 13/03447-6 - Combinatorial structures, optimization, and algorithms in theoretical Computer Science |
| Grantee: | Carlos Eduardo Ferreira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 13/21744-8 - Theoretical and Pratical Approaches to Packing Problems |
| Grantee: | Rafael Crivellari Saliba Schouery |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 13/02434-8 - Combinatorial optimization problems: packing and related problems |
| Grantee: | Flávio Keidi Miyazawa |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |