Abstract
We study the problem of minimizing the makespan for the precedence multiprocessor constrained scheduling problem with hierarchical communications [1]. We propose an 8/5-approximation algorithm for the UET-UCT (Unit Execution Time Unit Communication Time) hierarchical problem with an unbounded number of biprocessor machines. Moreover, we extend this result in the case where each cluster has m processors (where m is a fixed constant) by presenting an ρ-approximation algorithm where ρ = (2−2/2m+1).
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References
E. Bampis, R. Giroudeau, and J.-C. König. Using duplication for the precedence constrained multiprocessor scheduling problem with hierarchical communications. In P. Amestoy, P. Berger, M. Daydé, I. Duff, V. Frayssé, L. Giraud, and D. Ruiz, editors, EuroPar’99 Parallel Processing, Lecture Notes in Computer Science, No. 1685, pages 369–372. Springer-Verlag, 1999.
E. Bampis, R. Giroudeau, and J.C. König. On the hardness of approximating the precedence constrained multiprocessor scheduling problem with hierarchical communications. Technical Report 34, Université d’Evry Val d’Essonne, submitted, 1999.
B. Chen, C.N. Potts, and G.J. Woeginger. A review of machine scheduling: complexity, algorithms and approximability. Technical Report Woe-29, TU Graz, 1998.
P. Chrétienne, E.J. Coffman Jr, J.K. Lenstra, and Z. Liu. Scheduling Theory and its Applications. Wiley, 1995.
M.R. Garey and D.S. Johnson. Computers and Intractability, a Guide to the Theory of NP-Completeness. Freeman, 1979.
R.L. Graham, E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnooy Kan. Optimization and approximation in deterministics sequencing and scheduling theory: a survey. Ann. Discrete Math., 5:287–326, 1979.
J.A. Hoogeveen, J.K. Lenstra, and B. Veltman. Three, four, five, six, or the complexity of scheduling with communication delays. O. R. Lett., 16(3), 1994.
A. Munier and J.C. König. A heuristic for a scheduling problem with communication delays. Operations Research, 45(1):145–148, 1997.
C. Picouleau. Etude des problèmes d’optimisation dans les systèmes distribués. PhD thesis, Université de Paris VI, 1992.
B. Veltman. Multiprocessor scheduling with communications delays. PhD thesis, CWI-Amsterdam, Holland, 1993.
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Bampis, E., Giroudeau, R., König, JC. (2000). An Approximation Algorithm for the Precedence Constrained Scheduling Problem with Hierarchical Communications. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_37
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DOI: https://doi.org/10.1007/3-540-46541-3_37
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