一种基于MPI的复杂网络分层映射算法
An MPI-based Algorithm for Mapping Complex Networks onto Hierarchical Architectures
摘要：
在分布式内存系统上处理大量应用程序图需要将这些图映射到系统的处理元素（PE）上。当PE具有非统一的通信成本或输入高度不规则时，这项任务变得更加重要。通常情况下，映射是使用分区来解决的，分为两步或集成的方法。并行分区工具确实存在;然而，相应的映射算法或其公共实现都有主要的顺序部分或其他严重的扩展限制。在本文中，我们提出了一个并行算法，将图形映射到PE的分层系统。我们的解决方案集成了分区和映射，它以一种简洁的方式作为一个隐式标记树的系统层次结构模型。应用程序图的顶点也被标记，并且这些顶点标签诱导映射。映射优化遵循并行标签传播的基本思想，但我们调整标签变化的增益计算，以快速考虑所引起的通信成本。我们基于MPI的代码是第一个公开实现的并行图映射算法，为此，我们扩展了分区库ParHIP。为了评估我们的算法的实现，我们在百万和十亿级范围内的复杂网络进行比较实验。在一般情况下，我们的映射工具显示了良好的可扩展性高达几千个PE。与其他基于MPI的竞争对手相比，我们的算法实现了最佳的速度和质量的权衡，我们的质量结果甚至优于非并行映射工具。
英文摘要：
Processing massive application graphs on distributed memory systems requires to map the graphs onto the system's processing elements (PEs). This task becomes all the more important when PEs have non-uniform communication costs or the input is highly irregular. Typically, mapping is addressed using partitioning, in a two-step approach or an integrated one. Parallel partitioning tools do exist; yet, corresponding mapping algorithms or their public implementations all have major sequential parts or other severe scaling limitations. In this paper, we propose a parallel algorithm that maps graphs onto the PEs of a hierarchical system. Our solution integrates partitioning and mapping; it models the system hierarchy in a concise way as an implicit labeled tree. The vertices of the application graph are labeled as well, and these vertex labels induce the mapping. The mapping optimization follows the basic idea of parallel label propagation, but we tailor the gain computations of label changes to quickly account for the induced communication costs. Our MPI-based code is the first public implementation of a parallel graph mapping algorithm; to this end, we extend the partitioning library ParHIP. To evaluate our algorithm's implementation, we perform comparative experiments with complex networks in the million- and billion-scale range. In general our mapping tool shows good scalability on up to a few thousand PEs. Compared to other MPI-based competitors, our algorithm achieves the best speed to quality trade-off and our quality results are even better than non-parallel mapping tools.
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