### 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: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings |

Pages | 204-217 |

Number of pages | 14 |

Volume | 4627 LNCS |

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) | 03029743 |

ISSN (Electronic) | 16113349 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings*(Vol. 4627 LNCS, pp. 204-217). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS).

**Approximation algorithms for the max-min allocation problem.** / Khot, Subhash; Ponnuswami, Ashok Kumar.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings.*vol. 4627 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4627 LNCS, pp. 204-217, 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, 8/20/07.

}

TY - GEN

T1 - Approximation algorithms for the max-min allocation problem

AU - Khot, Subhash

AU - Ponnuswami, Ashok Kumar

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38049084076&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38049084076&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540742074

VL - 4627 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 204

EP - 217

BT - Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings

ER -