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Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions

  • Subhash Khot
  • Richard J. Lipton
  • Evangelos Markakis
  • Aranyak Mehta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3828)

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.

Keywords

Utility Function Allocation Problem Proof System Combinatorial Auction Submodular Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Subhash Khot
    • 1
  • Richard J. Lipton
    • 1
  • Evangelos Markakis
    • 1
  • Aranyak Mehta
    • 1
  1. 1.Georgia Institute of TechnologyAtlantaUSA

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