Scheduling chain-structured tasks to minimize makespan and mean flow time

Authors:
Jianzhong Du;Joseph Y-T. Leung;Gilbert H. Young
Affiliations:
Computer Science Program, University of Texas at Dallas, Richardson, Texas 75083 USA;Computer Science Program, University of Texas at Dallas, Richardson, Texas 75083 USA;Computer Science Program, University of Texas at Dallas, Richardson, Texas 75083 USA
Venue:
Information and Computation
Year:
1991

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Abstract

We consider the problem of scheduling a set of chains onm 1 identical processors with the objectives of minimizing the makespan and the mean flow time. We show that finding a nonpreemptive schedule with the minimum makespan is strongly NP-hard for each fixedm 1, answering the open question of whether this problem is strongly NP-hard for trees. We also show that finding a nonpreemptive schedule with the minimum mean flow time is strongly NP-hard for each fixedm 1, improving the known strong NP-hardness results for in-trees and out-trees. Finally, we generalize the result of McNaughton, showing that preemption cannot reduce the mean weighted flow time for a set of chains. The last two results together imply that finding a preemptive schedule with the minimum mean flow time is also strongly NP-hard for each fixedm 1, answering another open question on the complexity of this problem for trees.