### 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) |
---|---|

Pages (from-to) | 3-18 |

Number of pages | 16 |

Journal | Algorithmica (New York) |

Volume | 52 |

Issue number | 1 |

DOIs | |

State | Published - Sep 2008 |

### Fingerprint

### Keywords

- Combinatorial auctions
- Hardness of approximation
- Social welfare
- Submodular

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Applied Mathematics
- Safety, Risk, Reliability and Quality

### Cite this

*Algorithmica (New York)*,

*52*(1), 3-18. https://doi.org/10.1007/s00453-007-9105-7

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

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 52, no. 1, pp. 3-18. https://doi.org/10.1007/s00453-007-9105-7

}

TY - JOUR

T1 - Inapproximability results for combinatorial auctions with submodular utility functions

AU - Khot, Subhash

AU - Lipton, Richard J.

AU - Markakis, Evangelos

AU - Mehta, Aranyak

PY - 2008/9

Y1 - 2008/9

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.

KW - Combinatorial auctions

KW - Hardness of approximation

KW - Social welfare

KW - Submodular

UR - http://www.scopus.com/inward/record.url?scp=49149102694&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49149102694&partnerID=8YFLogxK

U2 - 10.1007/s00453-007-9105-7

DO - 10.1007/s00453-007-9105-7

M3 - Article

VL - 52

SP - 3

EP - 18

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 1

ER -