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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.

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