Scheduling a Divisible Task in a Two-dimensional Toroidal Mesh

Abstract In this paper, a problem of scheduling an arbitrarily divisible task is considered. Taking into account both communication delays and computation time we propose a scheduling method which minimizes total execution time. We focus on two dimensional processor networks assuming a circuit-switching routing mechanism. The scheduling method uses a scattering scheme proposed in Peters and Syska (IEEE Trans. Parallel Distributed Systems 7(3) (1996) 246–255) to distribute parts of the task to processors in a minimum time. We show how to model and solve this problem with a set of algebraic equations. A solution of the latter allows one to analyze the performance of the network depending on various actual parameters of the task and the parallel machine. Though the method is defined for a particular architecture and scattering scheme it can be generalized to analyze other architectures of parallel computer systems.

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