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On the hardness of approximating the UET-UCT scheduling problem with hierarchical communications

Published online by Cambridge University Press:  15 July 2002

Evripidis Bampis ,
R. Giroudeau  and
J.-C. König
Evripidis Bampis
Affiliation:
Laboratoire de Méthodes Informatiques (LaMI), Université d'Evry-Val-d'Essonne, UMR 8042 du CNRS, 523 place des Terrasses, Immeuble ÉVRY-II, 91000 Evry, France; bampis@lami.univ-evry.fr. giroudeau@lami.univ-evry.fr.
R. Giroudeau
Affiliation:
Laboratoire de Méthodes Informatiques (LaMI), Université d'Evry-Val-d'Essonne, UMR 8042 du CNRS, 523 place des Terrasses, Immeuble ÉVRY-II, 91000 Evry, France; bampis@lami.univ-evry.fr. giroudeau@lami.univ-evry.fr.
J.-C. König
Affiliation:
LIRMM, Université de Montpellier II, UMR 5506 du CNRS, 161 rue Ada, 34392 Montpellier Cedex 5, France; konig@lirmm.fr.
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Abstract

We consider the unit execution time unit communication time (UET-UCT) scheduling model with hierarchical communica tions [CITE], and we study the impact of the hierarchical communications hypothesis on the hardness of approximation. We prove that there is no polynomial time approximation algorithm with performance guarantee smaller than 5/4 (unless P = NP). This result is an extension of the result of Hoogeveen et al. [CITE] who proved that there is no polynomial time ρ-approximation algorithm with p < 7/6 for the classical UET-UCT scheduling problem with homogeneous communication delays and an unrestricted number of identical machines.

Keywords

Schedulinghierarchical communicationsnon-approxima bility.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 1 , January 2002 , pp. 21 - 36
Copyright
© EDP Sciences, 2002

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References

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Hoogeveen, J.A., Lenstra, J.K. and Veltman, B.. Three, four, Five, six, or the complexity of scheduling with communication delays. Oper. Res. Lett. 16 (1994) 129-137. CrossRef