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 2008

Fingerprint

Combinatorial Auctions
Submodular Function
Inapproximability
Approximation algorithms
Welfare
Utility Function
Polynomials
Proof System
Monotone Function
Polynomial-time Algorithm
Approximation Algorithms
Maximise

Keywords

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

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Applied Mathematics
  • Safety, Risk, Reliability and Quality

Cite this

Inapproximability results for combinatorial auctions with submodular utility functions. / Khot, Subhash; Lipton, Richard J.; Markakis, Evangelos; Mehta, Aranyak.

In: Algorithmica (New York), Vol. 52, No. 1, 09.2008, p. 3-18.

Research output: Contribution to journalArticle

Khot, Subhash ; Lipton, Richard J. ; Markakis, Evangelos ; Mehta, Aranyak. / Inapproximability results for combinatorial auctions with submodular utility functions. In: Algorithmica (New York). 2008 ; Vol. 52, No. 1. pp. 3-18.
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