Abstract
It is known that task scheduling problem of a complete k-ary intree with unit time tasks and general communication delays onto an unlimited number of processors is NP-complete. In this paper, we show that such a problem can be solved in linear time if we restrict communication delays within the range from (k − 1) to k unit times. We also show that naive scheduling is optimal if communication delays are constant and at most (k − 1) unit times.
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Ahmad, I. and Kwok, Y.: On Exploiting Task Duplication in Parallel Program Scheduling, IEEE Trans. on Parallel and Distributed Systems, Vol. 9, No. 9 (1998) 872–892
Blazewicz, J., Guinand, F., Penz, B., and Trystram, D.: Scheduling Complete Trees on Two Uniform Processors with Integer Speed Ratios and Communication Delays, Parallel Processing Letters, Vol. 10, No. 4 (2000) 267–277
Chrétienne, P.: A Polynomial Algorithm to Optimally Schedule Tasks on a Virtual Distributed System under Tree-like Precedence Constraints, European J. Oper. Res. Vol. 43 (1989) 225–230
Chrétienne, P. and Picouleau, C.: Scheduling with Communication Delays: A Survey, Scheduling Theory and Its Applications, Wiley (1995) 65–90
Colin, J. Y. and Chritienne, P.: C.P.M. Scheduling with Small Communication Delays and Task Duplication, Operations Research, Vol. 39, No. 4 (1991) 680–684
Darbha, S. and Agrawal, D. P.: Optimal Scheduling Algorithm for Distributed-Memory Machines, IEEE Trans. on Parallel and Distributed Systems, Vol. 9, No. 1 (1998) 87–95
El-Rewini, H., Lewis, T.G., and Ali, H.H.: TASK SCHEDULING in PARALLEL and DISTRIBUTED SYSTEMS, PTR Prentice Hall (1994)
Gerasoulis, A. and Yang, T.: On the Granularity and Clustering of Directed Acyclic Task Graphs, IEEE Transactions on Parallel and Distributed Systems, Vol. 4, No. 6 (1993) 686–701
Graham, R. L., Lawler, E. L., Lenstra, J. K., and Rinnooy Kan, A. H. G.: Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey, Ann. Discrete Math. Vol. 5 (1979) 287–326
Guinand, F. and Trystram, D.: Optimal Scheduling of UECT Trees on Two Processors, RAIRO Operations Research, Vol. 34, No. 2(2000) 131–144
Jakoby, A. and Reischuk, R.: The Complexity of Scheduling Problems with Communication Delays for Trees, Lecture Notes in Computer Science, Vol. 621. Springer-Verlag (1992) 165–177
Jung, H., Kirousis, L., and Spirakis, P.: Lower bounds and Efficient Algorithms for Multiprocessor Scheduling of Dags with Communication Delays, the Information and Computation Journal, Vol. 105, No. 1 (1993) 94–104
Lawler, E. L.: Scheduling Trees on Multiprocessors with Unit Communication Delays, Presented at the First Workshop on Models and Algorithms for Planning and Scheduling Problems, Villa Vigoni, Lake Como, Italy, unpublished manuscript, June (1993)
Lenstra, J. K., Veldhorst, M., and Veltman, B.: The Complexity of Scheduling Trees with Communication Delays, Journal of Algorithms, Vol. 20 (1996) 157–173
Picouleau, C.: Etude de Problèmes les Systèmes Distribués, Ph.D. thesis, Univ. Piere et Marie Curie, Paris, France (1992)
Thurimella, R. and Yesha, Y.: A scheduling principle for precedence graphs with communication delay, International Conference on Parallel Processing, 3 (1992) 229–236
Varvarigou, T. A., Roychowdhury, V. P., Kailath, T., and Lawler, E.: Scheduling In and Out Forests in the Presence of Communication Delays, IEEE Trans. on Parallel and Distributed Systems, Vol. 7, No. 10 (1996) 1065–1074
Yang, T. and Gerasoulis, A.: DSC: Scheduling Parallel Tasks on an Unbounded Number of Processors, IEEE Trans. on Parallel and Distributed Systems, Vol. 5, No. 9 (1994) 951–967
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Fujimoto, N., Hagihara, K. (2002). Optimal Task Scheduling of a Complete K-Ary Tree with Communication Delays. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_8
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DOI: https://doi.org/10.1007/3-540-48086-2_8
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