Inapproximability results for combinatorial auctions with submodular utility functions

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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)
Title of host publicationInternet and Network Economics - First International Workshop, WINE 2005, Proceedings
Pages92-101
Number of pages10
Volume3828 LNCS
DOIs
StatePublished - 2005
Event1st International Workshop on Internet and Network Economics, WINE 2005 - Hong Kong, China
Duration: Dec 15 2005Dec 17 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3828 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other1st International Workshop on Internet and Network Economics, WINE 2005
CountryChina
CityHong Kong
Period12/15/0512/17/05

Fingerprint

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Khot, S., Lipton, R. J., Markakis, E., & Mehta, A. (2005). Inapproximability results for combinatorial auctions with submodular utility functions. In Internet and Network Economics - First International Workshop, WINE 2005, Proceedings (Vol. 3828 LNCS, pp. 92-101). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3828 LNCS). https://doi.org/10.1007/11600930_10

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

Internet and Network Economics - First International Workshop, WINE 2005, Proceedings. Vol. 3828 LNCS 2005. p. 92-101 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3828 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Khot, S, Lipton, RJ, Markakis, E & Mehta, A 2005, Inapproximability results for combinatorial auctions with submodular utility functions. in Internet and Network Economics - First International Workshop, WINE 2005, Proceedings. vol. 3828 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3828 LNCS, pp. 92-101, 1st International Workshop on Internet and Network Economics, WINE 2005, Hong Kong, China, 12/15/05. https://doi.org/10.1007/11600930_10
Khot S, Lipton RJ, Markakis E, Mehta A. Inapproximability results for combinatorial auctions with submodular utility functions. In Internet and Network Economics - First International Workshop, WINE 2005, Proceedings. Vol. 3828 LNCS. 2005. p. 92-101. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11600930_10
Khot, Subhash ; Lipton, Richard J. ; Markakis, Evangelos ; Mehta, Aranyak. / Inapproximability results for combinatorial auctions with submodular utility functions. Internet and Network Economics - First International Workshop, WINE 2005, Proceedings. Vol. 3828 LNCS 2005. pp. 92-101 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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