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Autour de nouvelles notions pour l'analyse desalgorithmes d'approximation : formalisme unifié et classes d'approximation

Published online by Cambridge University Press:  15 April 2003

Marc Demange  and
Vangelis Paschos
Marc Demange
Affiliation:
ESSEC, Cergy-Pontoise, France; demange@essec.fr.
Vangelis Paschos
Affiliation:
LAMSADE, Université Paris-Dauphine, France; paschos@lamsade.dauphine.fr.
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Abstract

Cet article est le premier d'une série de deux articles où nous présentons les principales caractéristiques d'un nouveau formalisme pour l'approximation polynomiale (algorithmique polynomiale à garanties de performances pour les problèmes NP-difficiles). Ce travail est l'occasion d'un regard critique sur ce domaine et de discussions sur la pertinence des notions usuelles. Il est aussi l'occasion de se familiariser avec l'approximation polynomiale, de comprendre ses enjeux et ses méthodes. Ces deux articles s'adressent donc autant aux spécialistes qu'aux non spécialistes de ce domaine. Nous insistons tout particulièrement sur l'intérêt, tant théorique qu'opérationnel, de mettre en évidence une structure au sein de la classe NPO des problèmes d'optimisation de NP. Dans ce premier article, nous nous intéressons aux outils qui permettent d'évaluer, dans l'absolu, les propriétés d'approximation de problèmes difficiles. Nous discutons notamment les notions de chaînes d'approximation, de niveau d'approximation, d'ordre de difficulté ainsi que deux notions de limites (par rapport à une suite d'algorithmes et par rapport aux instances). Chaque notion est largement discutée et illustrée par de nombreux exemples choisis essentiellement pour leur valeur pédagogique.
 Mots Clés. Complexité, difficulté intrinsèque, analyse des algorithmes et des problèmes, algorithmes d'approximation. Classification Mathématique. 68Q15, 68Q17, 68Q25, 68W25.

Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 3 , July 2002 , pp. 237 - 277
Copyright
© EDP Sciences, 2002

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