Inapproximability of maximum r-regular induced connected subgraph problems

Yuichi Asahiro, Hiroshi Eto, Eiji Miyano

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Given a connected graph G = (V, E) on n vertices, the Maximum r-Regular Induced Connected Subgraph (r-MaxRICS) problem asks for a maximum sized subset of vertices S ⊆ V such that the induced subgraph G[S] on S is connected and r-regular. It is known that 2-MaxRICS and 3-MaxRICS are NP-hard. Moreover, 2-MaxRICS cannot be approximated within a factor of n1-ε in polynomial time for any ε > 0 unless P = NP. In this paper, we show that r-MaxRICS are NP-hard for any fixed integer r ≥ 4. Furthermore, we show that for any fixed integer r ≥ 3, r-MaxRICS cannot be approximated within a factor of n1/6-ε in polynomial time for any ε > 0 unless P = NP.

Original languageEnglish
Pages (from-to)443-449
Number of pages7
JournalIEICE Transactions on Information and Systems
VolumeE96-D
Issue number3
DOIs
Publication statusPublished - Mar 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence

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