Mapping virtual processes onto physical processos is one of the most important issues in parallel computing. The problem of mapping of processes/tasks onto processors is equivalent to the graph embedding problem which has been studied extensively. Although many techniques have been proposed for embeddings of two-dimensional grids, hypercubes, etc., there are few efforts on embeddings of three-dimensional grids and tori. Motivated for better support of task mapping for Blue Gene/L supercomputer, in this paper, we present embedding and integration techniques for the embeddings of three-dimensional grids and tori. The topology mapping library that based on such techniques generates high-quality embeddings of two/three-dimensional grids/tori. In addition, the library is used in BG/L MPI library for scalable support of MPI topology functions. With extensive empirical studies on large scale systems against popular benchmarks and real applications, we demonstrate that the library can significantly improve the communication performance and the scalability of applications.

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