### 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 language | English |
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Pages (from-to) | 2501-2516 |

Number of pages | 16 |

Journal | Discrete Applied Mathematics |

Volume | 156 |

Issue number | 13 |

DOIs | |

Publication status | Published - 2008 Jul 6 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*156*(13), 2501-2516. https://doi.org/10.1016/j.dam.2008.03.015