Inapproximability results for combinatorial auctions with submodular utility functions

Subhash Khot, Richard J. Lipton, Evangelos Markakis, Aranyak Mehta

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)3-18
Number of pages16
JournalAlgorithmica (New York)
Volume52
Issue number1
DOIs
StatePublished - Sep 1 2008

Keywords

  • Combinatorial auctions
  • Hardness of approximation
  • Social welfare
  • Submodular

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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