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)


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.


Utility Function Allocation Problem Proof System Combinatorial Auction Submodular Function 
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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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