使用通信高效稀疏矩阵乘法缩放介数中心性
Scaling betweenness centrality using communication-efficient sparse matrix multiplication
摘要：
介数中心性（BC）是一个重要的图问题，它通过穿过顶点的最短路径的数量来衡量顶点的重要性。我们提出了最大边界介数中心性（MFBC）：一种基于新颖的稀疏矩阵乘法例程的简洁BC算法，其在$p$处理器上执行比最佳已知替代方案少$p^{1/3}$倍的通信，对于具有$n$顶点和平均度$k=n/p^{2/3}$的图。我们制定，实施，并证明了MFBC的正确性加权图利用幺半群，而不是半环，这使得一个令人惊讶的简洁的配方。MFBC的规模非常稀疏和相对密集的图形。它自动搜索分布式数据分解和稀疏矩阵乘法算法的空间，以获得最有利的配置。MFBC实现的性能比著名的CombBLAS库高出8倍，并显示出更强大的性能。我们的设计方法很容易扩展到其他图形问题。
英文摘要：
Betweenness centrality (BC) is a crucial graph problem that measures the significance of a vertex by the number of shortest paths leading through it. We propose Maximal Frontier Betweenness Centrality (MFBC): a succinct BC algorithm based on novel sparse matrix multiplication routines that performs a factor of $p^{1/3}$ less communication on $p$ processors than the best known alternatives, for graphs with $n$ vertices and average degree $k=n/p^{2/3}$. We formulate, implement, and prove the correctness of MFBC for weighted graphs by leveraging monoids instead of semirings, which enables a surprisingly succinct formulation. MFBC scales well for both extremely sparse and relatively dense graphs. It automatically searches a space of distributed data decompositions and sparse matrix multiplication algorithms for the most advantageous configuration. The MFBC implementation outperforms the well-known CombBLAS library by up to 8x and shows more robust performance. Our design methodology is readily extensible to other graph problems.
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