## Abstract

We develop for set cover games several general cost-sharing methods that are approximately budget-balanced, core, and/or group-strategyproof. We first study the cost sharing for a single set cover game, which does not have a budget-balanced core. We show that there is no cost allocation method that can always recover more than 1/In n of the total cost if we require the cost sharing being a core. Here n is the number of all players to be served. We give an efficient cost allocation method that always recovers 1/In n d_{max}- of the total cost, where d_{max} is the maximum size of all sets. We then study the cost allocation scheme for all induced subgames. It is known that no cost sharing scheme can always recover more than 1/n of the total cost for every subset of players. We give an efficient cost sharing scheme that always recovers at least 1/2n of the total cost for every subset of players and furthermore, our scheme is cross-monotone. When the elements to be covered are selfish agents with privately known valuations, we present a strategyproof charging mechanism, under the assumption that all sets are simple sets, such that each element maximizes its profit when it reports its valuation truthfully; further, the total cost of the set cover is no more than In d_{max} times that of an optimal solution. When the sets are selfish agents with privately known costs, we present a strategyproof payment mechanism in which each set maximizes its profit when it reports its cost truthfully. We also show how to fairly share the payments to all sets among the elements.

Original language | English |
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Title of host publication | STACS 2005 |

Subtitle of host publication | 22nd Annual Symposium on Theoretical Aspects of Computer Science, Stuttgart, Germany, February 24-26, 2004, Proceedings |

Editors | Volker Diekert, Bruno Durand |

Publisher | Springer-Verlag Berlin Heidelberg |

Pages | 218-230 |

Number of pages | 13 |

Edition | 1st |

ISBN (Electronic) | 9783540318569 |

ISBN (Print) | 9783540249986 |

DOIs | |

Publication status | Published - 2 Feb 2005 |

Externally published | Yes |

Event | 22nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2005 - Stuttgart, Germany Duration: 24 Feb 2005 → 26 Feb 2005 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer Verlag |

Volume | 3404 |

ISSN (Print) | 0302-9743 |

### Conference

Conference | 22nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2005 |
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Country/Territory | Germany |

City | Stuttgart |

Period | 24/02/05 → 26/02/05 |

## Scopus Subject Areas

- Theoretical Computer Science
- Computer Science(all)

## User-Defined Keywords

- Service Provider
- Greedy Algorithm
- Cost Sharing
- Cost Allocation
- Partial Cover