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Lineartime Approximation Schemes for Scheduling Malleable Parallel Tasks
 Proceedings of the 10th Annual ACMSIAM Symposium on Discrete Algorithms
, 1999
"... A malleable parallel task is one whose execution time is a function of the number of (identical) processors alloted to it. We study the problem of scheduling a set of n independent malleable tasks on a xed number of parallel processors, and propose an approximation scheme that for any xed > 0, comp ..."
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A malleable parallel task is one whose execution time is a function of the number of (identical) processors alloted to it. We study the problem of scheduling a set of n independent malleable tasks on a xed number of parallel processors, and propose an approximation scheme that for any xed > 0, computes in O(n) time a nonpreemptive schedule of length at most (1 + ) times the optimum. 1 Introduction In this paper, we study the following scheduling problem. Suppose there is given a set of tasks T = fT 0 ; : : : ; T n 1 g and a set of identical processors M = f1; : : : ; mg. Each task T j has an associated function t j : M ! Q + that gives the execution time t j (`) of task T j in terms of the number of processors ` 2 M that are assigned to T j . Given j processors alloted to task T j , these j processors are required to execute task T j in union and without preemption, i.e. they all have to start processing task T j at some starting time j , and complete it at j + t j (...