An Approximate Algorithm for the Partitionable Independent Task Scheduling Problem

Scheduling a collection of tasks on a multiprocessor, consisting of p processors, that minimizes the maximum completion time has attracted a lot of attention in the literature [12]. In this paper, we introduce a new problem of scheduling a collection of independent tasks on a multiprocessor, called the partitionable independent task scheduling problem. Associated with each task, we are given the time it takes to run on a uniprocessor, and speedup that can be obtained by running it on i processors, 1≤i ≤p . We present an approximate algorithm that guarantees a solution within (1+1/p ) 2 3333333 of the optimal solution, under a reasonable assumption on the speedup functions.