### Abstract

For an integer d ≥ 2, a distance-d independent set of an unweighted graph G = (V,E) is a subset S ⊆ V of vertices such that for any pair of vertices u, v ∈ S, the number of edges in any path between u and v is at least d in G. Given an unweighted graph G, the goal of Maximum Distance-d Independent Set problem (MaxDdIS) is to find a maximum-cardinality distance-d independent set of G. In this paper we focus on MaxD3IS on cubic (3-regular) graphs. For every fixed integer d ≥ 3, MaxDdIS is NP-hard even for planar bipartite graphs of maximum degree three. Furthermore, when d = 3, it is known that there exists no σ-approximation algorithm for MaxD3IS oncubic graphs for constant σ < 1. 00105. On the other hand, the previously best approximation ratio known for MaxD3IS on cubic graphs is 2. In this paper, we improve the approximation ratio into 1.875 for MaxD3IS on cubic graphs.

Original language | English |
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Title of host publication | WALCOM |

Subtitle of host publication | Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings |

Editors | Md. Saidur Rahman, Hsu-Chun Yen, Sheung-Hung Poon |

Publisher | Springer Verlag |

Pages | 228-240 |

Number of pages | 13 |

ISBN (Print) | 9783319539249 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Event | 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 - Hsinchu, Taiwan, Province of China Duration: Mar 29 2017 → Mar 31 2017 |

### 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 | 10167 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 |
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Country | Taiwan, Province of China |

City | Hsinchu |

Period | 3/29/17 → 3/31/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings*(pp. 228-240). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10167 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-53925-6_18

**Approximation algorithm for the distance-3 independent set problem on cubic graphs.** / Eto, Hiroshi; Ito, Takehiro; Liu, Zhilong; Miyano, Eiji.

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

*WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10167 LNCS, Springer Verlag, pp. 228-240, 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017, Hsinchu, Taiwan, Province of China, 3/29/17. https://doi.org/10.1007/978-3-319-53925-6_18

}

TY - GEN

T1 - Approximation algorithm for the distance-3 independent set problem on cubic graphs

AU - Eto, Hiroshi

AU - Ito, Takehiro

AU - Liu, Zhilong

AU - Miyano, Eiji

PY - 2017/1/1

Y1 - 2017/1/1

N2 - For an integer d ≥ 2, a distance-d independent set of an unweighted graph G = (V,E) is a subset S ⊆ V of vertices such that for any pair of vertices u, v ∈ S, the number of edges in any path between u and v is at least d in G. Given an unweighted graph G, the goal of Maximum Distance-d Independent Set problem (MaxDdIS) is to find a maximum-cardinality distance-d independent set of G. In this paper we focus on MaxD3IS on cubic (3-regular) graphs. For every fixed integer d ≥ 3, MaxDdIS is NP-hard even for planar bipartite graphs of maximum degree three. Furthermore, when d = 3, it is known that there exists no σ-approximation algorithm for MaxD3IS oncubic graphs for constant σ < 1. 00105. On the other hand, the previously best approximation ratio known for MaxD3IS on cubic graphs is 2. In this paper, we improve the approximation ratio into 1.875 for MaxD3IS on cubic graphs.

AB - For an integer d ≥ 2, a distance-d independent set of an unweighted graph G = (V,E) is a subset S ⊆ V of vertices such that for any pair of vertices u, v ∈ S, the number of edges in any path between u and v is at least d in G. Given an unweighted graph G, the goal of Maximum Distance-d Independent Set problem (MaxDdIS) is to find a maximum-cardinality distance-d independent set of G. In this paper we focus on MaxD3IS on cubic (3-regular) graphs. For every fixed integer d ≥ 3, MaxDdIS is NP-hard even for planar bipartite graphs of maximum degree three. Furthermore, when d = 3, it is known that there exists no σ-approximation algorithm for MaxD3IS oncubic graphs for constant σ < 1. 00105. On the other hand, the previously best approximation ratio known for MaxD3IS on cubic graphs is 2. In this paper, we improve the approximation ratio into 1.875 for MaxD3IS on cubic graphs.

UR - http://www.scopus.com/inward/record.url?scp=85014231181&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014231181&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-53925-6_18

DO - 10.1007/978-3-319-53925-6_18

M3 - Conference contribution

AN - SCOPUS:85014231181

SN - 9783319539249

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

SP - 228

EP - 240

BT - WALCOM

A2 - Rahman, Md. Saidur

A2 - Yen, Hsu-Chun

A2 - Poon, Sheung-Hung

PB - Springer Verlag

ER -