An algorithm for flow time minimization and its asymptotic makespan properties

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Abstract

This paper develops an algorithm for assigning n jobs to k identical machines. The algorithm minimizes the mean flow time and asymptotically minimizes the makespan. The absolute difference between the optimal makespan and the heuristic makespan is bounded by O(log n/n) almost surely when job processing times are independently and uniformly distributed on [0, 1]. The ratio between these two makespans approaches one almost surely when processing times are independent, identically distributed random variables with a finite mean.

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