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.
Mots clés : scheduling, non-approximability, processor network model
@article{RO_2012__46_1_1_0,
author = {Boudet, Vincent and Cohen, Johanne and Giroudeau, Rodolphe and K\"onig, Jean-Claude},
title = {Scheduling in the presence of processor networks : complexity and approximation},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {1--22},
publisher = {EDP-Sciences},
volume = {46},
number = {1},
year = {2012},
doi = {10.1051/ro/2012005},
mrnumber = {2934890},
zbl = {1242.90075},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2012005/}
}
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 - Recherche Opérationnelle PY - 2012 SP - 1 EP - 22 VL - 46 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2012005/ DO - 10.1051/ro/2012005 LA - en ID - RO_2012__46_1_1_0 ER -
%0 Journal Article %A Boudet, Vincent %A Cohen, Johanne %A Giroudeau, Rodolphe %A König, Jean-Claude %T Scheduling in the presence of processor networks : complexity and approximation %J RAIRO - Operations Research - Recherche Opérationnelle %D 2012 %P 1-22 %V 46 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2012005/ %R 10.1051/ro/2012005 %G en %F RO_2012__46_1_1_0
Boudet, Vincent; Cohen, Johanne; Giroudeau, Rodolphe; König, Jean-Claude. Scheduling in the presence of processor networks : complexity and approximation. RAIRO - Operations Research - Recherche Opérationnelle, Tome 46 (2012) no. 1, pp. 1-22. doi : 10.1051/ro/2012005. http://archive.numdam.org/articles/10.1051/ro/2012005/
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