Approximability of the distance independent set problem on regular graphs and planar graphs

Hiroshi Eto, Takehiro Ito, Zhilong Liu, Eiji Miyano

研究成果: Conference contribution

9 被引用数 (Scopus)

抄録

This paper studies generalized variants of the maximum independent set problem, called the Maximum Distance-d Independent Set problem (MaxDdIS for short). 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 MaxDdIS is to find a maximum-cardinality distance-d independent set of G. In this paper, we analyze the (in)approximability of the problem on r-regular graphs (r ≥ 3) and planar graphs, as follows: (1) For every fixed integers d ≥ 3 and r ≥ 3, MaxDdIS on r-regular graphs is APX-hard. (2) We design polynomial-time O(rd−1)-approximation and O(rd−2/d)- approximation algorithms for MaxDdIS on r-regular graphs. (3) We sharpen the above O(rd−2/d)-approximation algorithms when restricted to d = r = 3, and give a polynomial-time 2-approximation algorithm for MaxD3IS on cubic graphs. (4) Finally, we show that MaxDdIS admits a polynomial-time approximation scheme (PTAS) for planar graphs.

本文言語English
ホスト出版物のタイトルCombinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings
編集者Minming Li, Lusheng Wang, T-H. Hubert Chan
出版社Springer Verlag
ページ270-284
ページ数15
ISBN(印刷版)9783319487489
DOI
出版ステータスPublished - 2016
イベント10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016 - Hong Kong, China
継続期間: 2016 12 162016 12 18

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
10043 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016
国/地域China
CityHong Kong
Period16/12/1616/12/18

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

フィンガープリント

「Approximability of the distance independent set problem on regular graphs and planar graphs」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル