### Abstract

The Max-Min allocation problem is to distribute indivisible goods to people so as to maximize the minimum utility of the people. We show a (2k - 1)-approximation algorithm for Max-Min when there are k people with subadditive utility functions. We also give a fc/a-approximation algorithm (for α < k/2) if the utility functions are additive and the utility of an item for a person is restricted to 0, 1 or U for some U > 1. The running time of this algorithm depends exponentially on the parameter α. Both the algorithms are combinatorial, simple and easy to analyze.

Original language | English (US) |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization |

Subtitle of host publication | Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings |

Publisher | Springer Verlag |

Pages | 204-217 |

Number of pages | 14 |

ISBN (Print) | 9783540742074 |

DOIs | |

State | Published - 2007 |

Event | 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 - Princeton, NJ, United States Duration: Aug 20 2007 → Aug 22 2007 |

### 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 | 4627 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 |
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Country | United States |

City | Princeton, NJ |

Period | 8/20/07 → 8/22/07 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Khot, S., & Ponnuswami, A. K. (2007). Approximation algorithms for the max-min allocation problem. In

*Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings*(pp. 204-217). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-74208-1_15