On the approximability of the range assignment problem on radio networks in presence of selfish agents

  • Authors:
  • Christoph Ambühl;Andrea E. F. Clementi;Paolo Penna;Gianluca Rossi;Riccardo Silvestri

  • Affiliations:
  • Istituto "Dalle Molle" di Studi sull'Intelligenza Artificiale, Manno, Switzerland;Dipartimento di Matematica, Università degli Studi "Tor Vergata" di Roma, Italy;Dipartimento di Informatica ed Applicazioni "R.M. Capocelli", Università degli Studi di Salerno, Italy;Dipartimento di Matematica, Università degli Studi "Tor Vergata" di Roma, Italy;Dipartimento di Informatica, Università degli Studi "La Sapienza" di Roma, Italy

  • Venue:
  • Theoretical Computer Science - Game theory meets theoretical computer science
  • Year:
  • 2005
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Abstract

We consider the range assignment problem in ad-hoc wireless networks in the context of selfish agents: A network manager aims to assigning transmission ranges to the stations in order to achieve strong connectivity of the network within a minimal overallpower consumption. Station is not directly controlled by the manager and may refuse to transmit with a certain transmission range because it might be costly in terms of power consumption.We investigate the existence of payment schemes which induce the stations to follow the decisions of a network manager in computing a range assignment, that is, truthful mechanisms for the range assignment problem. We provide both positive and negative results on the existence of truthful VCG-based mechanisms for this NP-hard problem. We prove that (i) in general, every polynomial-time truthful VCG-based mechanism computes a solution of cost far-off the optimum, unless P = NP and (ii) there exists a polynomial-time truthful VCG-based mechanism achieving constant approximation for practically relevant, still NP-hard versions, i.e., the metric and the well-spread case.