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Scheduling in the presence of processor networks : complexity and approximation

Published online by Cambridge University Press:  04 May 2012

Vincent Boudet ,
Johanne Cohen ,
Rodolphe Giroudeau  and
Jean-Claude König
Vincent Boudet
Affiliation:
LIRMM, 161 rue Ada, 34392 Montpellier Cedex 5, UMR 5055, France. boudet@lirmm.fr; rgirou@lirmm.fr; konig@lirmm.fr
Johanne Cohen
Affiliation:
LORIA, 54506 Vandoeuvre-lès-Nancy Cedex, France; Johanne.Cohen@loria.fr
Rodolphe Giroudeau
Affiliation:
LIRMM, 161 rue Ada, 34392 Montpellier Cedex 5, UMR 5055, France. boudet@lirmm.fr; rgirou@lirmm.fr; konig@lirmm.fr
Jean-Claude König
Affiliation:
LIRMM, 161 rue Ada, 34392 Montpellier Cedex 5, UMR 5055, France. boudet@lirmm.fr; rgirou@lirmm.fr; konig@lirmm.fr
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Abstract

In this paper, we study the problem of makespan minimization for the multiprocessor scheduling problem in the presence of communication delays. The communication delay between two tasks i and j depends on the distance between the two processors on which these two tasks are executed. Lahlou shows that a simple polynomial-time algorithm exists when the length of the schedule is at most two (the problem becomes 𝒩𝒫-complete when the length of the schedule is at most three). We prove that there is no polynomial-time algorithm with a performance guarantee of less than 4/3 (unless 𝒫 = 𝒩𝒫) to minimize the makespan when the network topology is a chain or ring and the precedence graph is a bipartite graph of depth one. We also develop two polynomial-time approximation algorithms with constant ratio dedicated to cases where the processor network admits a limited or unlimited number of processors.

Keywords

Schedulingnon-approximabilityprocessor network model
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 1 , January 2012 , pp. 1 - 22
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

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