Hostname: page-component-cb9f654ff-9b74x Total loading time: 0 Render date: 2025-08-26T11:54:52.382Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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