As the high performance computing systems scale up, mapping the tasks of a parallel application onto physical processors to allow efficient communication becomes one of the critical performance issues. Existing algorithms were usually designed to map applications with regular communication patterns. Their mapping criterion usually overlooks the size of communicated messages, which is the primary factor of communication time. In addition, most of their time complexities are too high to process large scale problems. In this paper, we present a hierarchical mapping algorithm (HMA), which is capable of mapping applications with irregular communication patterns. It first partitions tasks according to their run-time communication information. The tasks that communicate with each others more frequently are regarded as strongly connected. Based on their connectivity strength, the tasks are partitioned into supernodes based on the algorithms in spectral graph theory. The hierarchical partitioning reduces the mapping algorithm complexity to achieve scalability. Finally, the run-time communication information will be used again in fine tuning to explore better mappings. With the experiments, we show how the mapping algorithm helps to reduce the point-to-point communication time for the PDGEMM, a ScaLAPACK matrix multiplication computation kernel, up to 20% and the AMG2006, a tier 1 application of the Sequoia benchmark, up to 7%.
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