### 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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Pages (from-to) | 3-18 |

Number of pages | 16 |

Journal | Algorithmica (New York) |

Volume | 52 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1 2008 |

### Keywords

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

### ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics

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## Cite this

Khot, S., Lipton, R. J., Markakis, E., & Mehta, A. (2008). Inapproximability results for combinatorial auctions with submodular utility functions.

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