Abstract
This work presents approximation algorithms for scheduling the tasks of a parallel application that are subject to precedence constraints. The considered tasks are malleable which means that they may be executed on a varying number of processors in parallel. The considered objective criterion is the makespan, i.e., the largest task completion time.
We demonstrate a close relationship between this scheduling problem and one of its subproblems, the allotment problem. By exploiting this relationship, we design a polynomial time approximation algorithm with performance guarantee arbitrarily close to \( {{\left( {3 + \sqrt 5 } \right)} \mathord{\left/ {\vphantom {{\left( {3 + \sqrt 5 } \right)} {2 \approx 2.61803}}} \right. \kern-\nulldelimiterspace} {2 \approx 2.61803}} \) for the special case of series parallel precedence constraints and for the special case of precedence constraints of bounded width. These special cases cover the important situation of tree structured precedence constraints. For the general case with arbitrary precedence constraints, we give a polynomial time approximation algorithm with performance guarantee \( 3 + \sqrt 5 \approx 5.23606 \).
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References
E. Blayo, L. Debreu, G. Mounié, and D. Trystram [1999]. Dynamic load balancing for ocean circulation with adaptive meshing. Proceedings of the 5th European Conference on Parallel Computing, Springer LNCS 1685, 303–312.
M. Cosnard and D. Trystram [1995]. Parallel Algorithms and Architectures. International Thomson Publishing.
D. Culler, R. Karp, D. Patterson, A. Sahay, E. Santos, K. Schauser, R. Subramanian, AND T. Von Eicken [1996]. LogP: A practical model of parallel computation. Communications of the ACM 39, 78–85.
P. De, E.J. Dunne, J.B. Gosh, AND C.E. Wsells [1995]. The discrete time-cost tradeoff problem revisited. European Journal of Operational Research 81, 225–238.
P. De, E.J. Dunne, J.B. Gosh, AND C.E. Wsells [1997]. Complexity of the discrete time-cost tradeoff problem for project networks. Operations Research 45, 302–306.
M. Drozdowski [1996]. Scheduling multiprocessor tasks-An overview. European Journal of Operational Research 94, 215–230.
J. Du AND J.Y.-T. Leung [1989]. Complexity of scheduling parallel task systems. SIAM Journal on Discrete Mathematics 2, 473–487.
A. Gerasoulis AND T. Yang [1992]. PYRROS: Static scheduling and code generation for message passing multiprocessors. Proceedings of the 6th ACM International Conference on Super computing, 428–437.
R.L. Graham [1966]. Bounds for certain multiprocessing anomalies. Bell System Technical Journal 45, 1563–1581.
J.K. Lenstra AND A.H.G. Rinnooy Kan [1978]. Complexity of scheduling under precedence constraints. Operations Research 26, 22–35.
R. Lepére, G. Mounie, Robič, AND D. Trystram [1999]. Malleable tasks: An electromagnetic efficient model for solving actual parallel applications. Proceedings of the International Conference on Parallel Computing 99 (Parco’99), Imperial College Press, 598–605.
G.N.S. Prasanna and B.R. Musicus [1991]. Generalized multiprocessor scheduling using optimal control. Proceedings of the 3rd Annual Symposium on Parallel Algorithms and Architectures (SPAA’91), 216–228.
M. Skutella [1998]. Approximation algorithms for the discrete time-cost tradeoff problem. Mathematics of Operations Research 23, 909–929.
J. Turek, J. Wolf, and P. Yu [1992]. Approximate algorithms for scheduling parallelizable tasks. Proceedings of the 4th Annual Symposium on Parallel Algorithms and Architectures (SPAA’ 92), 323–332.
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© 2001 Springer-Verlag Berlin Heidelberg
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Lepére, R., Trystram, D., Woeginger, G.J. (2001). Approximation Algorithms for Scheduling Malleable Tasks under Precedence Constraints. In: auf der Heide, F.M. (eds) Algorithms — ESA 2001. ESA 2001. Lecture Notes in Computer Science, vol 2161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44676-1_12
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DOI: https://doi.org/10.1007/3-540-44676-1_12
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