## Abstract

In the classical maximum independent set problem, we are given a graph G of "conflicts" and are asked to find a maximum conflict-free subset. If we think of the remaining nodes as being "assigned" (at unit cost each) to one of these independent vertices and ask for an assignment of minimum cost, this yields the vertex cover problem. In this paper, we consider a more general scenario where the assignment costs might be given by a distance metric d (which can be unrelated to G) on the underlying set of vertices. This problem, in addition to being a natural generalization of vertex cover and an interesting variant of the κ-median problem, also has connection to constrained clustering and database repair. Understanding the relation between the conflict structure (the graph) and the distance structure (the metric) for this problem turns out to be the key to isolating its complexity. We show that when the two structures are unrelated, the problem inherits a trivial upper bound from vertex cover and provide an almost matching lower bound on hardness of approximation. We then prove a number of lower and upper bounds that depend on the relationship between the two structures, including polynomial time algorithms for special graphs.

Original language | English |
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Title of host publication | Leibniz International Proceedings in Informatics, LIPIcs |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Pages | 401-412 |

Number of pages | 12 |

Volume | 24 |

ISBN (Electronic) | 9783939897644 |

DOIs | |

Publication status | Published - 1 Dec 2013 |

MoE publication type | A4 Article in a conference publication |

Event | International Conference on Foundations of Software Technology and Theoretical Computer Science - Guwahati, India Duration: 12 Dec 2013 → 14 Dec 2013 Conference number: 33 |

### Conference

Conference | International Conference on Foundations of Software Technology and Theoretical Computer Science |
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Abbreviated title | FSTTCS |

Country | India |

City | Guwahati |

Period | 12/12/2013 → 14/12/2013 |

## Keywords

- Approximation algorithms
- Clustering
- Vertex cover