Parallel machine scheduling with uncertain communication delays
RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 1, pp. 1-16.

This paper is concerned with scheduling when the data are not fully known before the execution. In that case computing a complete schedule off-line with estimated data may lead to poor performances. Some flexibility must be added to the scheduling process. We propose to start from a partial schedule and to postpone the complete scheduling until execution, thus introducing what we call a stabilization scheme. This is applied to the m machine problem with communication delays: in our model an estimation of the delay is known at compile time; but disturbances due to network contention, link failures, ... may occur at execution time. Hence the processor assignment and a partial sequencing on each processor are determined off-line. Some theoretical results for tree-like precedence constraints and an experimental study show the interest of this approach compared with fully on-line scheduling.

DOI : https://doi.org/10.1051/ro:2003011
Classification : 90B35,  90B25
Mots clés : parallel computing, scheduling with communication delays, disturbances on communication delays, list scheduling, flexibility
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Moukrim, Aziz; Sanlaville, Eric; Guinand, Frédéric. Parallel machine scheduling with uncertain communication delays. RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 1, pp. 1-16. doi : 10.1051/ro:2003011. http://www.numdam.org/articles/10.1051/ro:2003011/

[1] E. Bampis, F. Guinand and D. Trystram, Some Models for Scheduling Parallel Programs with Communication Delays. Discrete Appl. Math. 51 (1997) 5-24. | MR 1424523 | Zbl 0863.68015

[2] Ph. Chrétienne, A polynomial algorithm to optimally schedule tasks on a virtual distributed system under tree-like precedence constraints. EJOR 43 (1989) 225-230. | MR 1033650 | Zbl 0689.90045

[3] Ph. Chrétienne and C. Picouleau, Scheduling with communication delays: a survey, in Scheduling Theory and its Applications, edited by Ph. Chrétienne, E.G. Coffman, J.K. Lenstra and Z. Liu. John Wiley Ltd. (1995). | MR 1376609

[4] E.G. Coffman Jr. and R.L. Graham, Optimal scheduling for two-processor systems. Acta Informatica 1 (1972) 200-213. | MR 334913 | Zbl 0248.68023

[5] G.L. Djordjevic and M.B. Tosic, A heuristic for scheduling task graphs with communication delays onto multiprocessors. Parallel Comput. 22 (1996) 1197-1214. | MR 1426112 | Zbl 0875.68083

[6] G. Galambos and G.J. Woeginger, An on-line scheduling heuristic with better worst case ratio than Graham list scheduling. SIAM J. Comput. 22 (1993) 349-355. | MR 1207790 | Zbl 0781.90051

[7] A. Gerasoulis and T. Yang, A Comparison of Clustering Heuristics for Scheduling DAGs on Multiprocessors. J. Parallel Distributed Comput. 16 (1992) 276-291. | MR 1196593 | Zbl 0797.68021

[8] A. Gerasoulis and T. Yang, Application of graph scheduling techniques in parallelizing irregular scientific computation, in Parallel Algorithms for Irregular Problems: State of the Art, edited by A. Ferreira and J. Rolim. Kluwer Academic Publishers, The Netherlands (1995). | Zbl 0856.68130

[9] F. Guinand and D. Trystram, Optimal scheduling of UECT trees on two processors. RAIRO: Oper. Res. 34 (2000) 131-144. | Numdam | MR 1755979 | Zbl 0961.90032

[10] C. Hanen and A. Munier, Performance of Coffman Graham schedule in the presence of unit communication delays. Discrete Appl. Math. 81 (1998) 93-108. | MR 1492003 | Zbl 0894.68012

[11] J.J. Hwang, Y.C. Chow, F.D. Anger and C.Y. Lee, Scheduling precedence graphs in systems with interprocessor communication times. SIAM J. Comput. 18 (1989) 244-257. | MR 986664 | Zbl 0677.68026

[12] A.W.J. Kolen, A.H.G. Rinnooy Kan, C.P.M. Van Hoesel and A.P.M. Wagelmans, Sensitivity analysis of list scheduling heuristics. Discrete Appl. Math. 55 (1994) 145-162. | MR 1301856 | Zbl 0824.90082

[13] P. Kouvelis and G. Yu, Robust Discrete Optimization and Its Applications. Kluwer Academic Publisher (1997). | MR 1480918 | Zbl 0873.90071

[14] J.K. Lenstra, M. Veldhorst and B. Veltman, The complexity of scheduling trees with communication delays. J. Algorithms 20 (1996) 157-173. | MR 1368721 | Zbl 0840.68013

[15] A. Moukrim and A. Quilliot, Scheduling with communication delays and data routing in Message Passing Architectures. Springer, Lecture Notes in Comput. Sci. 1388 (1998) 438-451.

[16] C.H. Papadimitriou and M. Yannakakis, Towards an Architecture-Independent Analysis of Parallel Algorithms. SIAM J. Comput. 19 (1990) 322-328. | MR 1042731 | Zbl 0692.68032

[17] V.J. Rayward-Smith, UET scheduling with interprocessor communication delays. Discrete Appl. Math. 18 (1986) 55-71. | Zbl 0634.90031

[18] V. Sarkar, Partitioning and Scheduling Parallel Programs for Execution on Multiprocessors. The MIT Press (1989).

[19] G.C. Sih and E.A. Lee, A compile-time scheduling heuristic for interconnection-constrained heterogeneous processor architectures. IEEE Trans. Parallel Distributed Systems 4 (1993) 279-301.

[20] Y.N. Sotskov, A.P.M. Wagelmans and F. Werner, On the calculation of stability radius of an optimal or an approximate schedule. Ann. O.R. 83 (1998) 213-252. | MR 1661683 | Zbl 0911.90222

[21] S.D. Wu, E. Byeon and R.H. Storer, A graph-theoretic decomposition of the job shop scheduling problem to achieve scheduling robustness. Oper. Res. 47 (1999) 113-124. | MR 1689986 | Zbl 0979.90030

[22] T. Yang and A. Gerasoulis, List scheduling with and without communication delay. Parallel Comput. 19 (1993) 1321-1344. | Zbl 0797.68020

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