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

5 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
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

Fingerprint

Approximability
Approximation algorithms
Independent Set
Regular Graph
Planar graph
Approximation Algorithms
Polynomials
Polynomial time
Inapproximability
Maximum Independent Set
Polynomial Time Approximation Scheme
Integer
Cubic Graph
Graph in graph theory
Cardinality
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. (2016). Approximability of the distance independent set problem on regular graphs and planar graphs. In M. Li, L. Wang, & T-H. H. Chan (Eds.), Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings (pp. 270-284). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10043 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-48749-6_20

Approximability of the distance independent set problem on regular graphs and planar graphs. / Eto, Hiroshi; Ito, Takehiro; Liu, Zhilong; Miyano, Eiji.

Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings. ed. / Minming Li; Lusheng Wang; T-H. Hubert Chan. Springer Verlag, 2016. p. 270-284 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10043 LNCS).

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

Eto, H, Ito, T, Liu, Z & Miyano, E 2016, Approximability of the distance independent set problem on regular graphs and planar graphs. in M Li, L Wang & T-HH Chan (eds), Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10043 LNCS, Springer Verlag, pp. 270-284, 10th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2016, Hong Kong, China, 12/16/16. https://doi.org/10.1007/978-3-319-48749-6_20
Eto H, Ito T, Liu Z, Miyano E. Approximability of the distance independent set problem on regular graphs and planar graphs. In Li M, Wang L, Chan T-HH, editors, Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings. Springer Verlag. 2016. p. 270-284. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-48749-6_20
Eto, Hiroshi ; Ito, Takehiro ; Liu, Zhilong ; Miyano, Eiji. / Approximability of the distance independent set problem on regular graphs and planar graphs. Combinatorial Optimization and Applications - 10th International Conference, COCOA 2016, Proceedings. editor / Minming Li ; Lusheng Wang ; T-H. Hubert Chan. Springer Verlag, 2016. pp. 270-284 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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