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Truthful Mechanism Design for Multidimensional Covering Problems

  • Hadi Minooei
  • Chaitanya Swamy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7695)

Abstract

We investigate multidimensional covering mechanism-design problems, wherein there are m items that need to be covered and n agents who provide covering objects, with each agent i having a private cost for the covering objects he provides. The goal is to select a set of covering objects of minimum total cost that together cover all the items.

We focus on two representative covering problems: uncapacitated facility location (UFL) and vertex cover (VC). For multidimensional UFL, we give a black-box method to transform any Lagrangian-multiplier-preserving ρ-approximation algorithm for UFL to a truthful-in-expectation, ρ-approx. mechanism. This yields the first result for multidimensional UFL, namely a truthful-in-expectation 2-approximation mechanism.

For multidimensional VC (Multi-VC), we develop a decomposition method that reduces the mechanism-design problem into the simpler task of constructing threshold mechanisms, which are a restricted class of truthful mechanisms, for simpler (in terms of graph structure or problem dimension) instances of Multi-VC. By suitably designing the decomposition and the threshold mechanisms it uses as building blocks, we obtain truthful mechanisms with approximation ratios (n is the number of nodes): (1) O(logn) for Multi-VC on any minor-closed family of graphs; and (2) O(r 2logn) for r-dimensional VC on any graph. These are the first truthful mechanisms for Multi-VC with non-trivial approximation guarantees.

Keywords

Approximation Ratio Covering Problem Vertex Cover Combinatorial Auction Threshold Mechanism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hadi Minooei
    • 1
  • Chaitanya Swamy
    • 1
  1. 1.Combinatorics and OptimizationUniv. WaterlooWaterlooCanada

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