### Abstract

We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodular function, we prove that there is no polynomial time approximation algorithm which approximates the maximum social welfare by a factor better than 1 - 1/e ≃ 0.632, unless P= NP. Our result is based on a reduction from a multi-prover proof system for MAX-3-COLORING.

Original language | English (US) |
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Title of host publication | Internet and Network Economics - First International Workshop, WINE 2005, Proceedings |

Pages | 92-101 |

Number of pages | 10 |

Volume | 3828 LNCS |

DOIs | |

State | Published - 2005 |

Event | 1st International Workshop on Internet and Network Economics, WINE 2005 - Hong Kong, China Duration: Dec 15 2005 → Dec 17 2005 |

### 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 | 3828 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 1st International Workshop on Internet and Network Economics, WINE 2005 |
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Country | China |

City | Hong Kong |

Period | 12/15/05 → 12/17/05 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Internet and Network Economics - First International Workshop, WINE 2005, Proceedings*(Vol. 3828 LNCS, pp. 92-101). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3828 LNCS). https://doi.org/10.1007/11600930_10

**Inapproximability results for combinatorial auctions with submodular utility functions.** / Khot, Subhash; Lipton, Richard J.; Markakis, Evangelos; Mehta, Aranyak.

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

*Internet and Network Economics - First International Workshop, WINE 2005, Proceedings.*vol. 3828 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3828 LNCS, pp. 92-101, 1st International Workshop on Internet and Network Economics, WINE 2005, Hong Kong, China, 12/15/05. https://doi.org/10.1007/11600930_10

}

TY - GEN

T1 - Inapproximability results for combinatorial auctions with submodular utility functions

AU - Khot, Subhash

AU - Lipton, Richard J.

AU - Markakis, Evangelos

AU - Mehta, Aranyak

PY - 2005

Y1 - 2005

N2 - We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodular function, we prove that there is no polynomial time approximation algorithm which approximates the maximum social welfare by a factor better than 1 - 1/e ≃ 0.632, unless P= NP. Our result is based on a reduction from a multi-prover proof system for MAX-3-COLORING.

AB - We consider the following allocation problem arising in the setting of combinatorial auctions: a set of goods is to be allocated to a set of players so as to maximize the sum of the utilities of the players (i.e., the social welfare). In the case when the utility of each player is a monotone submodular function, we prove that there is no polynomial time approximation algorithm which approximates the maximum social welfare by a factor better than 1 - 1/e ≃ 0.632, unless P= NP. Our result is based on a reduction from a multi-prover proof system for MAX-3-COLORING.

UR - http://www.scopus.com/inward/record.url?scp=33744918055&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744918055&partnerID=8YFLogxK

U2 - 10.1007/11600930_10

DO - 10.1007/11600930_10

M3 - Conference contribution

SN - 3540309004

SN - 9783540309000

VL - 3828 LNCS

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

SP - 92

EP - 101

BT - Internet and Network Economics - First International Workshop, WINE 2005, Proceedings

ER -