### 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) |
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Title of host publication | Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings |

Pages | 484-493 |

Number of pages | 10 |

DOIs | |

State | Published - Dec 26 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) |
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Volume | 7074 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 22nd International Symposium on Algorithms and Computation, ISAAC 2011 |
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Country | Japan |

City | Yokohama |

Period | 12/5/11 → 12/8/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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

}

*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.

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

TY - GEN

T1 - Packing-based approximation algorithm for the k-set cover problem

AU - Fürer, Martin

AU - Yu, Huiwen

PY - 2011/12/26

Y1 - 2011/12/26

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84055217282&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84055217282&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-25591-5_50

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

M3 - Conference contribution

AN - SCOPUS:84055217282

SN - 9783642255908

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 484

EP - 493

BT - Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings

ER -