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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

Bampis, E., Giroudeau, R. and König, J.C., Using duplication for multiprocessor scheduling problem with hierarchical communications. Parallel Process. Lett. 10 (2000) 133-140. CrossRef
B. Chen, C.N. Potts and G.J. Woeginger, A review of machine scheduling: Complexity, algorithms and approximability, Technical Report Woe-29. TU Graz (1998).
Ph. Chrétienne, E.J. Coffman Jr., J.K. Lenstra and Z. Liu, Scheduling Theory and its Applications. Wiley (1995).
M.R. Garey and D.S. Johnson, Computers and Intractability, a Guide to the Theory of NP-Completeness. Freeman (1979).
Graham, R.L., Lawler, E.L., Lenstra, J.K. and Rinnooy Kan, A.H.G., Optimization and approximation in deterministics sequencing and scheduling theory: A survey. Ann. Discrete Math. 5 (1979) 287-326. CrossRef
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