PTAS-completeness in standard and differential approximation (Preliminary version)

نویسندگان

  • Cristina Bazgan
  • Bruno Escoffier
  • Vangelis Th. Paschos
چکیده

Nous nous plaçons dans le cadre de l’approximation polynomiale des problèmes d’optimisation. Les réductions préservant l’approximabilité ont permis de structurer les classes d’approximation classiques (APX, PTAS,...) en introduisant des notions de complétude. Par exemple, des problèmes naturels ont été montrés APXou DAPX-complets (pour le paradigme de l’approximation différentielle), sous des réductions préservant l’existence de schémas d’approximation polynomiaux. Nous introduisons ici une notion de PTAS-complétude pour laquelle des problèmes naturels sont PTAS-complets. Nous définissons également une notion analogue de DPTAS-complétude pour l’approximation différentielle, et montrons l’existence de problèmes DPTAS-complets naturels. Ensuite, nous étudions l’existence de problèmes intermédiaires (sous nos réductions) et répondons partiellement à la question en montrant que l’existence de problème NPO-intermediaires sous la réduction de Turing est une condition suffisante. Enfin, nous montrons que MIN COLORING est DAPX-complet sous la DPTAS-réduction (définie dans “G. Ausiello, C. Bazgan, M. Demange, et V. Th. Paschos, Completeness in differential approximation classes, MFCS’03”).

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تاریخ انتشار 2008