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Truthful Allocation in Graphs and Hypergraphs

Authors George Christodoulou, Elias Koutsoupias , Annamária Kovács



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Author Details

George Christodoulou
  • University of Liverpool, UK
Elias Koutsoupias
  • University of Oxford, UK
Annamária Kovács
  • Goethe University, Frankfurt am Main, Germany

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George Christodoulou, Elias Koutsoupias, and Annamária Kovács. Truthful Allocation in Graphs and Hypergraphs. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 56:1-56:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ICALP.2021.56

Abstract

We study truthful mechanisms for allocation problems in graphs, both for the minimization (i.e., scheduling) and maximization (i.e., auctions) setting. The minimization problem is a special case of the well-studied unrelated machines scheduling problem, in which every given task can be executed only by two pre-specified machines in the case of graphs or a given subset of machines in the case of hypergraphs. This corresponds to a multigraph whose nodes are the machines and its hyperedges are the tasks. This class of problems belongs to multidimensional mechanism design, for which there are no known general mechanisms other than the VCG and its generalization to affine minimizers. We propose a new class of mechanisms that are truthful and have significantly better performance than affine minimizers in many settings. Specifically, we provide upper and lower bounds for truthful mechanisms for general multigraphs, as well as special classes of graphs such as stars, trees, planar graphs, k-degenerate graphs, and graphs of a given treewidth. We also consider the objective of minimizing or maximizing the L^p-norm of the values of the players, a generalization of the makespan minimization that corresponds to p = ∞, and extend the results to any p > 0.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
Keywords
  • Algorithmic Game Theory
  • Scheduling Unrelated Machines
  • Mechanism Design

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