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(Non)-Approximability for the Multi-criteria TSP(1,2)

  • Eric Angel
  • Evripidis Bampis
  • Laurent Gourvès
  • Jérôme Monnot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3623)

Abstract

Many papers deal with the approximability of multi-criteria optimization problems but only a small number of non-approximability results, which rely on NP-hardness, exist in the literature. In this paper, we provide a new way of proving non-approximability results which relies on the existence of a small size good approximating set (i.e. it holds even in the unlikely event of P=NP). This method may be used for several problems but here we illustrate it for a multi-criteria version of the traveling salesman problem with distances one and two (TSP(1,2)). Following the article of Angel et al. (FCT 2003) who presented an approximation algorithm for the bi-criteria TSP(1,2), we extend and improve the result to any number k of criteria.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Eric Angel
    • 1
  • Evripidis Bampis
    • 1
  • Laurent Gourvès
    • 1
  • Jérôme Monnot
    • 2
  1. 1.LaMI, CNRS UMR 8042Université d’Évry Val d’EssonneFrance
  2. 2.LAMSADE, CNRS UMR 7024Université de Paris-DauphineFrance

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