Fast Convex Decomposition for Truthful Social Welfare Approximation

  • Dennis Kraft
  • Salman Fadaei
  • Martin Bichler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8877)

Abstract

Approximating the optimal social welfare while preserving truthfulness is a well studied problem in algorithmic mechanism design. Assuming that the social welfare of a given mechanism design problem can be optimized by an integer program whose integrality gap is at most α, Lavi and Swamy [1] propose a general approach to designing a randomized α-approximation mechanism which is truthful in expectation. Their method is based on decomposing an optimal solution for the relaxed linear program into a convex combination of integer solutions. Unfortunately, Lavi and Swamy’s decomposition technique relies heavily on the ellipsoid method, which is notorious for its poor practical performance. To overcome this problem, we present an alternative decomposition technique which yields an α(1 + ε) approximation and only requires a quadratic number of calls to an integrality gap verifier.

Keywords

Convex decomposition Truthful in expectation Mechanism design Approximation algorithms 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dennis Kraft
    • 1
  • Salman Fadaei
    • 1
  • Martin Bichler
    • 1
  1. 1.Department of InformaticsTU MünchenMunichGermany

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