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

N1 - Funding Information:
This work is partially supported by JSPS KAKENHI Grant Numbers JP15J05484, JP15H00849, JP16K00004, and JP26330017.
Publisher Copyright:
© Springer International Publishing AG 2017.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017

Y1 - 2017

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.

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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

T2 - 11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017

Y2 - 29 March 2017 through 31 March 2017

ER -