On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming
Journal of the ACM (JACM)
Complexity of preemptive minsum scheduling on unrelated parallel machines
Journal of Algorithms
The complexity of mean flow time scheduling problems with release times
Journal of Scheduling
Polynomial algorithm for parallel machine mean flow time scheduling problem with release dates
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part IV
Parallel machine problems with equal processing times: a survey
Journal of Scheduling
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A set of jobs has to be scheduled on parallel uniform machines. Each machine can handle at most one job at a time. Each job becomes available for processing at its release date. All jobs have the same execution requirement, and each machine has a known speed. The processing of any job may be interrupted arbitrarily often and resumed later on any machine. We want to find a schedule that minimizes the sum of completion times, i.e., we consider problem Q|r"j,p"j=p,pmtn|@?C"j whose complexity status was open. In this paper, we give a polynomial algorithm for the above problem. The algorithm is based on a reduction of the scheduling problem to a linear program. The crucial condition for implementing the proposed reduction is the known order of job completion times.