Packing-based approximation algorithm for the k-set cover problem

Martin Fürer; Huiwen Yu

doi:10.1007/978-3-642-25591-5_50

Packing-based approximation algorithm for the k-set cover problem

Martin Fürer, Huiwen Yu

Eberly College of Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (SciVal)

Abstract

We present a packing-based approximation algorithm for the k-Set Cover problem. We introduce a new local search-based k-set packing heuristic, and call it Restricted k-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted k-Set Packing algorithm, our k-Set Cover algorithm is composed of the k-Set Packing heuristic [8] for k ≥ 7, Restricted k-Set Packing for k = 6,5,4 and the semi-local (2,1)-improvement [2] for 3-Set Cover. We show that our algorithm obtains a tight approximation ratio of H _k - 0.6402 + Θ(1/k), where H _k is the k-th harmonic number. For small k, our results are 1.8667 for k = 6, 1.7333 for k = 5 and 1.5208 for k = 4. Our algorithm improves the currently best approximation ratio for the k-Set Cover problem of any k ≥ 4.

Original language	English (US)
Title of host publication	Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings
Pages	484-493
Number of pages	10
DOIs	https://doi.org/10.1007/978-3-642-25591-5_50
State	Published - 2011
Event	22nd International Symposium on Algorithms and Computation, ISAAC 2011 - Yokohama, Japan Duration: Dec 5 2011 → Dec 8 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7074 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	22nd International Symposium on Algorithms and Computation, ISAAC 2011
Country/Territory	Japan
City	Yokohama
Period	12/5/11 → 12/8/11

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-25591-5_50

Cite this

Fürer, M., & Yu, H. (2011). Packing-based approximation algorithm for the k-set cover problem. In Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings (pp. 484-493). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS). https://doi.org/10.1007/978-3-642-25591-5_50

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abstract = "We present a packing-based approximation algorithm for the k-Set Cover problem. We introduce a new local search-based k-set packing heuristic, and call it Restricted k-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted k-Set Packing algorithm, our k-Set Cover algorithm is composed of the k-Set Packing heuristic [8] for k ≥ 7, Restricted k-Set Packing for k = 6,5,4 and the semi-local (2,1)-improvement [2] for 3-Set Cover. We show that our algorithm obtains a tight approximation ratio of H k - 0.6402 + Θ(1/k), where H k is the k-th harmonic number. For small k, our results are 1.8667 for k = 6, 1.7333 for k = 5 and 1.5208 for k = 4. Our algorithm improves the currently best approximation ratio for the k-Set Cover problem of any k ≥ 4.",

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Fürer, M & Yu, H 2011, Packing-based approximation algorithm for the k-set cover problem. in Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7074 LNCS, pp. 484-493, 22nd International Symposium on Algorithms and Computation, ISAAC 2011, Yokohama, Japan, 12/5/11. https://doi.org/10.1007/978-3-642-25591-5_50

Packing-based approximation algorithm for the k-set cover problem. / Fürer, Martin; Yu, Huiwen.
Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. 2011. p. 484-493 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Packing-based approximation algorithm for the k-set cover problem

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