Scheduling in the presence of processor networks : complexity and approximation

Vincent Boudet; Johanne Cohen; Rodolphe Giroudeau; Jean-Claude König

RAIRO - Operations Research (2012)

  • Volume: 46, Issue: 1, page 1-22
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Boudet, Vincent, et al. "Scheduling in the presence of processor networks : complexity and approximation." RAIRO - Operations Research 46.1 (2012): 1-22. <http://eudml.org/doc/276398>.

@article{Boudet2012,
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.},
author = {Boudet, Vincent, Cohen, Johanne, Giroudeau, Rodolphe, König, Jean-Claude},
journal = {RAIRO - Operations Research},
keywords = {Scheduling; non-approximability; processor network model; scheduling},
language = {eng},
month = {5},
number = {1},
pages = {1-22},
publisher = {EDP Sciences},
title = {Scheduling in the presence of processor networks : complexity and approximation},
url = {http://eudml.org/doc/276398},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Boudet, Vincent
AU - Cohen, Johanne
AU - Giroudeau, Rodolphe
AU - König, Jean-Claude
TI - Scheduling in the presence of processor networks : complexity and approximation
JO - RAIRO - Operations Research
DA - 2012/5//
PB - EDP Sciences
VL - 46
IS - 1
SP - 1
EP - 22
AB - 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.
LA - eng
KW - Scheduling; non-approximability; processor network model; scheduling
UR - http://eudml.org/doc/276398
ER -

References

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