Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions

Authors:
Subhash Khot;Richard J. Lipton;Evangelos Markakis;Aranyak Mehta
Affiliations:
Georgia Institute of Technology, 30332, Atlanta, GA, USA;Georgia Institute of Technology, 30332, Atlanta, GA, USA and Telcordia Research, 07960, Morristown, NJ, USA;University of Toronto, Dept. of Computer Science, 10 King’s College Road, M5S3G4, Toronto, ON, Canada;IBM Almaden Research Center, 650 Harry Rd, 95120, San Jose, CA, USA
Venue:
Algorithmica
Year:
2008

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Abstract

We consider the following allocation problem arising in thesetting of combinatorial auctions: a set of goods is to beallocated to a set of players so as to maximize the sum of theutilities of the players (i.e., the social welfare). In the casewhen the utility of each player is a monotone submodular function,we prove that there is no polynomial time approximation algorithmwhich approximates the maximum social welfare by a factor betterthan 11/e$\simeq$0.632, unless P=NP. Ourresult is based on a reduction from a multi-prover proof system forMAX-3-COLORING.