IEICE TRANSACTIONS on Information
Worst Case Analysis of Approximation Algorithm of Abrams et al. for the Set k-Cover Problem
Summary :
In this paper, we consider the problem of partitioning a given collection of node sets into k collections such that the average size of collections is the largest, where the size of a collection is defined as the cardinarity of the union of the subsets contained in the collection. More concretely, we give an upper bound on the performance ratio of an approximation algorithm proposed by Abrams et al., which is known to have a performance ratio of at least 1-1/e≅0.6321 where e is Napier's constant. The proposed upper bound is 1-(2-d+1√2)d+1/2 for any d≥1 provided that k=o(n) which approaches to 0.75 as d increases.
- Publication
- IEICE TRANSACTIONS on Information Vol.E97-D No.3 pp.399-405
- Publication Date
- 2014/03/01
- Publicized
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.E97.D.399
- Type of Manuscript
- Special Section PAPER (Special Section on Foundations of Computer Science —New Trends in Theory of Computation and Algorithm—)
- Category
- Optimizing Algorithms, Parallel and Distributed Computing
Authors
Satoshi FUJITA
Institute of Engineering
Keyword
Latest Issue
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Satoshi FUJITA, "Worst Case Analysis of Approximation Algorithm of Abrams et al. for the Set k-Cover Problem" in IEICE TRANSACTIONS on Information,
vol. E97-D, no. 3, pp. 399-405, March 2014, doi: 10.1587/transinf.E97.D.399.
Abstract: In this paper, we consider the problem of partitioning a given collection of node sets into k collections such that the average size of collections is the largest, where the size of a collection is defined as the cardinarity of the union of the subsets contained in the collection. More concretely, we give an upper bound on the performance ratio of an approximation algorithm proposed by Abrams et al., which is known to have a performance ratio of at least 1-1/e≅0.6321 where e is Napier's constant. The proposed upper bound is 1-(2-d+1√2)d+1/2 for any d≥1 provided that k=o(n) which approaches to 0.75 as d increases.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E97.D.399/_p
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@ARTICLE{e97-d_3_399,
author={Satoshi FUJITA, },
journal={IEICE TRANSACTIONS on Information},
title={Worst Case Analysis of Approximation Algorithm of Abrams et al. for the Set k-Cover Problem},
year={2014},
volume={E97-D},
number={3},
pages={399-405},
abstract={In this paper, we consider the problem of partitioning a given collection of node sets into k collections such that the average size of collections is the largest, where the size of a collection is defined as the cardinarity of the union of the subsets contained in the collection. More concretely, we give an upper bound on the performance ratio of an approximation algorithm proposed by Abrams et al., which is known to have a performance ratio of at least 1-1/e≅0.6321 where e is Napier's constant. The proposed upper bound is 1-(2-d+1√2)d+1/2 for any d≥1 provided that k=o(n) which approaches to 0.75 as d increases.},
keywords={},
doi={10.1587/transinf.E97.D.399},
ISSN={1745-1361},
month={March},}
Copy
TY - JOUR
TI - Worst Case Analysis of Approximation Algorithm of Abrams et al. for the Set k-Cover Problem
T2 - IEICE TRANSACTIONS on Information
SP - 399
EP - 405
AU - Satoshi FUJITA
PY - 2014
DO - 10.1587/transinf.E97.D.399
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E97-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2014
AB - In this paper, we consider the problem of partitioning a given collection of node sets into k collections such that the average size of collections is the largest, where the size of a collection is defined as the cardinarity of the union of the subsets contained in the collection. More concretely, we give an upper bound on the performance ratio of an approximation algorithm proposed by Abrams et al., which is known to have a performance ratio of at least 1-1/e≅0.6321 where e is Napier's constant. The proposed upper bound is 1-(2-d+1√2)d+1/2 for any d≥1 provided that k=o(n) which approaches to 0.75 as d increases.
ER -
English
