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IEEE Transactions on Computers
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SIAM Journal on Discrete Mathematics
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Discrete Applied Mathematics
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SIAM Journal on Computing
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STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
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Journal of the ACM (JACM)
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SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
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Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
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ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
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Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
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ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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We study the problem of scheduling a set of n independent parallel tasks on m processors, where in addition to the processing time there is a size associated with each task indicating that the task can be processed on any subset of processors of the given size. Based on a linear programming formulation, we propose an algorithm for computing a preemptive schedule with minimum makespan, and show that the running time of the algorithm depends polynomially on m and only linearly on n. Thus for any fixed m, an optimal preemptive schedule can be computed in O(n) time. We also present extensions of this approach to other (more general) scheduling problems with malleable tasks, release times, due dates and maximum lateness minimization.