The 0-1 inverse maximum stable set problem

Yerim Chung, Marc Demange

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8 Citations (Scopus)

Abstract

In this paper we study the 0-1 inverse maximum stable set problem, denoted by I S{0, 1}. Given a graph and a fixed stable set, it is to delete the minimum number of vertices to make this stable set maximum in the new graph. We also consider I S{0, 1} against a specific algorithm such as G r e e d y and 2 o p t, aiming to delete the minimum number of vertices so that the algorithm selects the given stable set in the new graph; we denote them by I S{0, 1}, g r e e d y and I S{0, 1}, 2 o p t, respectively. Firstly, we show that they are NP-hard, even if the fixed stable set contains only one vertex. Secondly, we achieve an approximation ratio of 2 - Θ (frac(1, sqrt(l o g Δ))) for I S{0, 1}, 2 o p t. Thirdly, we study the tractability of I S{0, 1} for some classes of perfect graphs such as comparability, co-comparability and chordal graphs. Finally, we compare the hardness of I S{0, 1} and I S{0, 1}, 2 o p t for some other classes of graphs.

Original languageEnglish
Pages (from-to)2501-2516
Number of pages16
JournalDiscrete Applied Mathematics
Volume156
Issue number13
DOIs
Publication statusPublished - 2008 Jul 6

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All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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