### Abstract

We study algorithms based on local improvements for the k-Set Packing problem. The well-known local improvement algorithm by Hurkens and Schrijver [14] has been improved by Sviridenko and Ward [15] from to k/2 + ∈ to k+2/3, and by Cygan [7] to k+1/3 + ∈ for any ∈ > 0. In this paper, we achieve the approximation ratio k+1/3 + ∈ for the k-Set Packing problem using a simple polynomial-time algorithm based on the method by Sviridenko and Ward [15]. With the same approximation guarantee, our algorithm runs in time singly exponential in 1/∈^{2}, while the running time of Cygan's algorithm [7] is doubly exponential in 1/∈. On the other hand, we construct an instance with locality gap k+1/3 for any algorithm using local improvements of size O(n^{1/5}), where is the total number of sets. Thus, our approximation guarantee is optimal with respect to results achievable by algorithms based on local improvements.

Original language | English (US) |
---|---|

Title of host publication | Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers |

Publisher | Springer Verlag |

Pages | 408-420 |

Number of pages | 13 |

ISBN (Print) | 9783319091730 |

DOIs | |

State | Published - Jan 1 2014 |

Event | 3rd International Symposium on Combinatorial Optimization, ISCO 2014 - Lisbon, Portugal Duration: Mar 5 2014 → Mar 7 2014 |

### Publication series

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

Volume | 8596 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd International Symposium on Combinatorial Optimization, ISCO 2014 |
---|---|

Country | Portugal |

City | Lisbon |

Period | 3/5/14 → 3/7/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers*(pp. 408-420). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8596 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-09174-7_35

}

*Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8596 LNCS, Springer Verlag, pp. 408-420, 3rd International Symposium on Combinatorial Optimization, ISCO 2014, Lisbon, Portugal, 3/5/14. https://doi.org/10.1007/978-3-319-09174-7_35

**Approximating the k-Set Packing problem by local improvements.** / Fürer, Martin; Yu, Huiwen.

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

TY - GEN

T1 - Approximating the k-Set Packing problem by local improvements

AU - Fürer, Martin

AU - Yu, Huiwen

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We study algorithms based on local improvements for the k-Set Packing problem. The well-known local improvement algorithm by Hurkens and Schrijver [14] has been improved by Sviridenko and Ward [15] from to k/2 + ∈ to k+2/3, and by Cygan [7] to k+1/3 + ∈ for any ∈ > 0. In this paper, we achieve the approximation ratio k+1/3 + ∈ for the k-Set Packing problem using a simple polynomial-time algorithm based on the method by Sviridenko and Ward [15]. With the same approximation guarantee, our algorithm runs in time singly exponential in 1/∈2, while the running time of Cygan's algorithm [7] is doubly exponential in 1/∈. On the other hand, we construct an instance with locality gap k+1/3 for any algorithm using local improvements of size O(n1/5), where is the total number of sets. Thus, our approximation guarantee is optimal with respect to results achievable by algorithms based on local improvements.

AB - We study algorithms based on local improvements for the k-Set Packing problem. The well-known local improvement algorithm by Hurkens and Schrijver [14] has been improved by Sviridenko and Ward [15] from to k/2 + ∈ to k+2/3, and by Cygan [7] to k+1/3 + ∈ for any ∈ > 0. In this paper, we achieve the approximation ratio k+1/3 + ∈ for the k-Set Packing problem using a simple polynomial-time algorithm based on the method by Sviridenko and Ward [15]. With the same approximation guarantee, our algorithm runs in time singly exponential in 1/∈2, while the running time of Cygan's algorithm [7] is doubly exponential in 1/∈. On the other hand, we construct an instance with locality gap k+1/3 for any algorithm using local improvements of size O(n1/5), where is the total number of sets. Thus, our approximation guarantee is optimal with respect to results achievable by algorithms based on local improvements.

UR - http://www.scopus.com/inward/record.url?scp=84905841259&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905841259&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-09174-7_35

DO - 10.1007/978-3-319-09174-7_35

M3 - Conference contribution

AN - SCOPUS:84905841259

SN - 9783319091730

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

SP - 408

EP - 420

BT - Combinatorial Optimization - Third International Symposium, ISCO 2014, Revised Selected Papers

PB - Springer Verlag

ER -