### 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 |
---|---|

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) |
---|---|

Volume | 10167 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 |
---|---|

Country | Taiwan, Province of China |

City | Hsinchu |

Period | 3/29/17 → 3/31/17 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

## Fingerprint Dive into the research topics of 'Approximation algorithm for the distance-3 independent set problem on cubic graphs'. Together they form a unique fingerprint.

## 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