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

Hiroshi Eto, Takehiro Ito, Zhilong Liu, Eiji Miyano

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

8 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings
EditorsMinming Li, Lusheng Wang, T-H. Hubert Chan
PublisherSpringer Verlag
Pages270-284
Number of pages15
ISBN (Print)9783319487489
DOIs
Publication statusPublished - Jan 1 2016
Externally publishedYes
Event10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016 - Hong Kong, China
Duration: Dec 16 2016Dec 18 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10043 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016
CountryChina
CityHong Kong
Period12/16/1612/18/16

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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