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Designing a Truthful Mechanism for a Spanning Arborescence Bicriteria Problem

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Combinatorial and Algorithmic Aspects of Networking (CAAN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 4235))

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Abstract

Let a communication network be modelled by a directed graph G=(V,E) of n nodes and m edges, and assume that each edge is owned by a selfish agent, which privately holds a pair of values associated with the edge, namely its cost and its length. In this paper we analyze the problem of designing a truthful mechanism for computing a spanning arborescence of G rooted at a fixed node r ∈V having minimum cost (as computed w.r.t. the cost function) among all the spanning arborescences rooted at r which satisfy the following constraint: for each node, the distance from r (as computed w.r.t. the length function) must not exceed a fixed bound associated with the node. First, we prove that the problem is hard to approximate within better than a logarithmic factor, unless NP admits slightly superpolynomial time algorithms. Then, we provide a truthful single-minded mechanism for the problem, which guarantees an approximation factor of (1+ε)(n–1), for any ε>0.

Work partially supported by the Research Project GRID.IT, funded by the Italian Ministry of Education, University and Research.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di L’Aquila, Italy

    Davide Bilò, Luciano Gualà & Guido Proietti

  2. Istituto di Analisi dei Sistemi ed Informatica, CNR, Roma, Italy

    Guido Proietti

Authors
  1. Davide Bilò
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  2. Luciano Gualà
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  3. Guido Proietti
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Bilò, D., Gualà, L., Proietti, G. (2006). Designing a Truthful Mechanism for a Spanning Arborescence Bicriteria Problem. In: Erlebach, T. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2006. Lecture Notes in Computer Science, vol 4235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11922377_3

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  • DOI: https://doi.org/10.1007/11922377_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-48822-4

  • Online ISBN: 978-3-540-48824-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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