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The Master-Slave Paradigm with Heterogeneous Processors
September 2003 (vol. 14 no. 9)
pp. 897-908

Abstract—In this paper, we revisit the master-slave tasking paradigm in the context of heterogeneous processors. We assume that communications are handled by a bus and, therefore, at most one communication can take place at a given time step. We present a polynomial algorithm that gives the optimal solution when a single communication is needed before the execution of the tasks on the slave processors. When communications are required both before and after the processing of the tasks, we show that the problem is strongly NP-Complete. In this case, we present a guaranteed approximation algorithm. Finally, we present asymptotically optimal algorithms when communications are required before the processing of each task, or both before and after the processing of each task.

[1] R. Andonie, A.T. Chronopoulos, D. Grosu, and H. Galmeanu, Distributed Backpropagation Neural Networks on a PVM Heterogeneous System Proc. Parallel and Distributed Computing and Systems Conf., pp. 555-560, 1998.
[2] S. Bataineh, T. Hsiung, and T.G. Robertazzi, Closed Form Solutions for Bus and Tree Networks of Processors Load Sharing a Divisible Job IEEE Trans. Computers, vol. 43, no. 10, pp. 1184-1196, Oct. 1994.
[3] O. Beaumont, V. Boudet, A. Petitet, F. Rastello, and Y. Robert, A Proposal for a Heterogeneous Cluster ScaLAPACK (Dense Linear Solvers) IEEE Trans. Computers, vol. 50, no. 10, pp. 1052-1070, 2001.
[4] O. Beaumont, V. Boudet, F. Rastello, and Y. Robert, “Matrix-Matrix Multiplication on Heterogeneous Platforms,” Proc. 2000 Int'l Conf. Parallel Processing (ICPP 2000), 2000.
[5] V. Bharadwaj, D. Ghose, V. Mani, and T.G. Robertazzi, Scheduling Divisible Loads in Parallel and Distributed Systems. IEEE Press, 1996.
[6] P. Boulet, J. Dongarra, F. Rastello, Y. Robert, and F. Vivien, Algorithmic Issues on Heterogeneous Computing Platforms Parallel Processing Letters, vol. 9, no. 2, pp. 197-213, 1999.
[7] P. Brucker, C. Dhaenens-Flipo, S. Knust, S.A. Kravchenko, and F. Werner, Complexity Results for Parallel Machine Problems with a Single Server Technical Report Reihe P, No. 219, Fachbereich Mathematik Informatik, Univ. Osnabrück, 2000.
[8] S. Charcranoon, T.G. Robertazzi, and S. Luryi, Optimizing Computing Costs Using Divisible Load Analysis IEEE Trans. Computers, vol. 49, no. 9, pp. 987-991, Sept. 2000.
[9] A.T. Chronopoulos and S. Jagannathan, A Distributed Discrete-Time Neural Network Architecture for Pattern Allocation and Control Proc. IPDPS Workshop Bioinspired Solutions to Parallel Processing Problems, 2002.
[10] M.R. Garey and D.S. Johnson, Computers and Intractability, a Guide to the Theory of NP-Completeness. W.H. Freeman and Company, 1991.
[11] A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, and V. Sunderam, PVM Parallel Virtual Machine: A Users' Guide and Tutorial for Networked Parallel Computing. MIT Press, 1996.
[12] M. Gondran and M. Minoux, Graphs and Algorithms. John Wiley and Sons, 1984.
[13] N. Hall, C.N. Potts, and C. Sriskandarajah, Parallel Machine Scheduling with a Common Server Discrete Applied Math., vol. 102, pp. 223-243, 2000.
[14] S. Hedetniemi, Open Problems in Combinatorial Optimization, World Wide Web Document, , year?
[15] J.E. Hopcroft and R.M. Karp, An$n^{5/2}$Algorithm for Maximum Matching in Bipartite Graphs SIAM J. Computing, vol. 2, no. 4, pp. 225-231, 1973.
[16] S.A. Kravchenko and F. Werner, Parallel Machine Scheduling Problems with a Single Server Math. Computational Modelling, vol. 26, pp. 1-11, 1997.
[17] H. Lee and M. Guignard, A Hybrid Bounding Procedure for the Workload Allocation Problem on Parallel Unrelated Machines with Setups J. Operational Research Soc., vol. 47, pp. 1247-1261, 1996.
[18] J. Sohn, T.G. Robertazzi, and S. Luryi, Optimizing Computing Costs Using Divisible Load Analysis IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 3, pp. 225-234, Mar. 1998.
[19] K. Soman, R. Fraczkiewicz, C. Mumenthaler, B. von Freyberg, and T. Schaumann and W. Braun, FANTOM (Fast Newton-Raphson Torsion Angle Minimizer), World Wide Web Document, , 2003.
[20] J.R. Stiles, T.M. Bartol, M.M. Salpeter, and M.M. Salpeter, Monte Carlo Simulation of Neuromuscular Transmitter Release Using MCell, a General Simulator of Cellular Physiological Processes Computational Neuroscience, pp. 279-284, 1998.
[21] J. Watts and S. Taylor, “A Practical Approach to Dynamic Load Balancing,” IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 3, pp. 235–248, Mar. 1998.
[22] D.B. West, Introduction to Graph Theory. Prentice Hall, 1996.
[23] W. Yu, The Two-Machine Flow Shop Problem with Delays and the One-Machine Total Tardiness Problem PhD thesis, Technishe Univ. Eidhoven, June 1996.

Index Terms:
Heterogeneous processors, master-slave tasking, communication, matching, complexity.
Olivier Beaumont, Arnaud Legrand, Yves Robert, "The Master-Slave Paradigm with Heterogeneous Processors," IEEE Transactions on Parallel and Distributed Systems, vol. 14, no. 9, pp. 897-908, Sept. 2003, doi:10.1109/TPDS.2003.1233712
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