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1 Bulletin of the Polish Academy of Sciences. Technical Sciences

1 2014

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Scheduling arbitrary number of malleable tasks on multiprocessor systems

Barketau M. S., Kovalyov M. Y., Węglarz J., Machowiak M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2014

Vol. 62, nr 2

255--261

The problem of scheduling n tasks in a multiprocessor system with m processors to minimize the makespan is studied. Tasks are malleable, which means that a task can be executed by several processors at a time, its processing speed depends on the number of allocated processors, and a set of processors allocated to the same task can change over time. The processing speed of a task is a strictly increasing function of the number of processors allocated to this task. The earlier studies considered the case n ≤ m. This paper presents results for arbitrary n and m including characterizations of a feasible domain and an optimal solution, polynomial time algorithms for strictly increasing convex and concave processing speed functions, and a combinatorial exponential algorithm for arbitrary strictly increasing functions.