Preemptable malleable task scheduling problem

The problem of optimal scheduling n independent malleable tasks in a parallel processor system is studied. It is assumed that an execution of any task can be preempted and the number of processors allocated to the same task can change during its execution. We present a rectangle packing algorithm, which converts an optimal solution for the relaxed problem, in which the number of processors allocated to a task is not required to be integer, into an optimal solution for the original problem in O(n) time.