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

Hiroshi Eto, Takehiro Ito, Zhilong Liu, Eiji Miyano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

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 languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings
EditorsMd. Saidur Rahman, Hsu-Chun Yen, Sheung-Hung Poon
PublisherSpringer Verlag
Pages228-240
Number of pages13
ISBN (Print)9783319539249
DOIs
Publication statusPublished - Jan 1 2017
Event11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 - Hsinchu, Taiwan, Province of China
Duration: Mar 29 2017Mar 31 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10167 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
CountryTaiwan, Province of China
CityHsinchu
Period3/29/173/31/17

Fingerprint

Cubic Graph
Approximation algorithms
Independent Set
Approximation Algorithms
Computational complexity
Graph in graph theory
Integer
Regular Graph
Best Approximation
Maximum Degree
Bipartite Graph
Planar graph
Cardinality
NP-complete problem
Path
Subset
Approximation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Eto, H., Ito, T., Liu, Z., & Miyano, E. (2017). Approximation algorithm for the distance-3 independent set problem on cubic graphs. In M. S. Rahman, H-C. Yen, & S-H. Poon (Eds.), 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.

WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings. ed. / Md. Saidur Rahman; Hsu-Chun Yen; Sheung-Hung Poon. Springer Verlag, 2017. p. 228-240 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10167 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Eto, H, Ito, T, Liu, Z & Miyano, E 2017, Approximation algorithm for the distance-3 independent set problem on cubic graphs. in MS Rahman, H-C Yen & S-H Poon (eds), 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
Eto H, Ito T, Liu Z, Miyano E. Approximation algorithm for the distance-3 independent set problem on cubic graphs. In Rahman MS, Yen H-C, Poon S-H, editors, WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings. Springer Verlag. 2017. p. 228-240. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-53925-6_18
Eto, Hiroshi ; Ito, Takehiro ; Liu, Zhilong ; Miyano, Eiji. / Approximation algorithm for the distance-3 independent set problem on cubic graphs. WALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings. editor / Md. Saidur Rahman ; Hsu-Chun Yen ; Sheung-Hung Poon. Springer Verlag, 2017. pp. 228-240 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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