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Mathematical Problems in Engineering
Volume 2013, Article ID 184706, 15 pages
Research Article

Multistep Scheduling Algorithm for Parallel and Distributed Processing in Heterogeneous Systems with Communication Costs

1Department of Mechanical Engineering and Intelligent Systems, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan
2Department of Computer Science, Kogakuin University, 1-24-2 Nishishinjuku, Shinjuku-ku, Tokyo 163-8677, Japan

Received 16 August 2013; Revised 22 October 2013; Accepted 23 October 2013

Academic Editor: Chin-Chia Wu

Copyright © 2013 Hitoshi Yamazaki et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We discuss a task scheduling problem in heterogeneous systems and propose a multistep scheduling algorithm to solve it. Existing scheduling algorithms formulated as 0-1 integer linear programming can be used to consider the optimality of task scheduling. However, they cannot address complicated relations among tasks or communication costs among processors. Therefore, we propose a scheduling algorithm that formulates communication costs as 0-1 integer linear programming. On the other hand, 0-1 integer linear programming takes a long time to calculate the scheduling results because it is NP-complete. Thus, scheduling time also needs to be decreased. A solution for decreasing scheduling time is a graph clustering which decomposes a large task graph into smaller subtask graphs (clusters). Also, it is important for parallel and distributed processing to find task parallelism in a task graph. Then, we also propose a clustering algorithm based on SCAN. SCAN is an algorithm for finding clusters in a network. The clustering algorithm based on SCAN can find task parallelism in a task graph. In numerical examples, we argue the following two points. First, our multistep scheduling algorithm resolves the scheduling problem in heterogeneous systems. Second, it is superior to the existing scheduling algorithms in terms of calculation time.