Polynomial-time approximation schemes for maximizing gross substitutes utility under budget constraints

Akiyoshi Shioura

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

1 Citation (Scopus)

Abstract

We consider the maximization of a gross substitutes utility function under budget constraints. This problem naturally arises in applications such as exchange economies in mathematical economics and combinatorial auctions in (algorithmic) game theory. We show that this problem admits a polynomial-time approximation scheme (PTAS). More generally, we present a PTAS for maximizing a discrete concave function called an M -concave function under budget constraints. Our PTAS is based on rounding an optimal solution of a continuous relaxation problem, which is shown to be solvable in polynomial time by the ellipsoid method. We also consider the maximization of the sum of two M -concave functions under a single budget constraint. This problem is a generalization of the budgeted max-weight matroid intersection problem to the one with a nonlinear objective function. We show that this problem also admits a PTAS.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2011 - 19th Annual European Symposium, Proceedings
Pages1-12
Number of pages12
DOIs
Publication statusPublished - 2011 Sep 20
Event19th Annual European Symposium on Algorithms, ESA 2011 - Saarbrucken, Germany
Duration: 2011 Sep 52011 Sep 9

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6942 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other19th Annual European Symposium on Algorithms, ESA 2011
CountryGermany
CitySaarbrucken
Period11/9/511/9/9

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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