### Abstract

Given an undirected graph with weights on its vertices, the k most vital nodes independent set problem consists of determining a set of k vertices whose removal results in the greatest decrease in the maximum weight of independent sets. We also consider the complementary problem, minimum node blocker independent set that consists of removing a subset of vertices of minimum size such that the maximum weight of independent sets in the remaining graph is at most a specified value. We show that these problems are NP-hard on bipartite graphs but polynomial-time solvable on unweighted bipartite graphs. Furthermore, these problems are polynomial also on graphs of bounded treewidth and cographs. A result on the non-existence of a ptas is presented, too.

Original language | English |
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Title of host publication | Combinatorial Algorithms - 21st International Workshop, IWOCA 2010, Revised Selected Papers |

Publisher | Springer Verlag |

Pages | 154-166 |

Number of pages | 13 |

ISBN (Print) | 9783642192210 |

DOIs | |

Publication status | Published - Jan 1 2011 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6460 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Fingerprint

### Keywords

- NP-hard
- bipartite graph
- bounded treewidth
- cograph
- complexity
- independent set
- most vital nodes
- ptas

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Combinatorial Algorithms - 21st International Workshop, IWOCA 2010, Revised Selected Papers*(pp. 154-166). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6460 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-19222-7_17