Inapproximability results for combinatorial auctions with submodular utility functions

被引：34

作者：

Khot, Subhash ^{[2
]}

Lipton, Richard J. ^{[2
,3
]}

Markakis, Evangelos ^{[1
]}

Mehta, Aranyak ^{[4
]}

机构：

[1] Univ Toronto, Dept Comp Sci, Toronto, ON M5S3G4, Canada

[2] Georgia Inst Technol, Atlanta, GA 30322 USA

[3] Telcordia Res, Morristown, NJ 07960 USA

[4] IBM Corp, Almaden Res Ctr, San Jose, CA 95120 USA

来源：

ALGORITHMICA | 2008年 / 52卷 / 01期

关键词：

combinatorial auctions; submodular; social welfare; hardness of approximation;

D O I：

10.1007/s00453-007-9105-7

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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 similar or equal to 0.632, unless P=NP. Our result is based on a reduction from a multi-prover proof system for MAX-3-COLORING.

引用

页码：3 / 18

页数：16

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