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Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions

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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.

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Authors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Subhash Khot & Richard J. Lipton

  2. Telcordia Research, Morristown, NJ, 07960, USA

    Richard J. Lipton

  3. Dept. of Computer Science, University of Toronto, 10 King’s College Road, Toronto, ON, M5S3G4, Canada

    Evangelos Markakis

  4. IBM Almaden Research Center, 650 Harry Rd, San Jose, CA, 95120, USA

    Aranyak Mehta

Authors
  1. Subhash Khot
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  2. Richard J. Lipton
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  3. Evangelos Markakis
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  4. Aranyak Mehta
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Corresponding author

Correspondence to Evangelos Markakis.

Additional information

This work was performed when all authors were at the Georgia Institute of Technology. A preliminary version of this work appears in Khot et al. (Workshop on internet and network economics, pp. 92–101, 2005)

R.J. Lipton’s research supported by NSF grant CCF-0431023.

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Khot, S., Lipton, R.J., Markakis, E. et al. Inapproximability Results for Combinatorial Auctions with Submodular Utility Functions. Algorithmica 52, 3–18 (2008). https://doi.org/10.1007/s00453-007-9105-7

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  • DOI: https://doi.org/10.1007/s00453-007-9105-7

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