基于BFS的分布式并行局部有向子图枚举算法
BFS based distributed algorithm for parallel local directed sub-graph enumeration
摘要：
估计子图的频率对于许多任务都很重要，包括子图同构、基于核的异常检测和网络结构分析。虽然提出了多种算法用于完全枚举或基于采样的估计，但这些方法在非常大的图中失败。并行化的最新进展允许在非常大的图中估计总的子图计数。计算与每个顶点相关联的每个子图的频率的任务也得到了无向图的优秀解决方案。然而，目前还没有很好的解决方案非常大的有向图。在这里，我们提出了VDMC（顶点特定的分布式图案计数）-一个完全分布式的算法，以最佳地计算所有的3和4顶点连接的有向图（子图图案）与每个顶点的图。VDMC对每个基序仅计数一次，并且其功效在计数的基序的数量上是线性的。它是完全并行的，在基于GPU的计算中是高效的。VDMC基于三个主要元素：1）对顶点进行排序并且仅对包含递增阶顶点的模体进行计数，2）基于组成模体的BFS的平均长度对模体进行子排序，以及3）对于整个图仅移除同构一次。我们在这里比较VDMC的分析估计的预期数量的图案，并显示其准确性。VDMC是一种高效的CPU和GPU代码，具有用于高效图形操作的新型数据结构。我们展示了VDMC和真实世界图形的功效。VDMC允许在大型图中每个顶点周围的子图频率的精确分析，并为扩展方法开辟了道路，直到现在仅限于数千条边的图到具有数百万条边及以上的图。GIT：https://github.com/louzounlab/graph-measures
英文摘要：
Estimating the frequency of sub-graphs is of importance for many tasks, including sub-graph isomorphism, kernel-based anomaly detection, and network structure analysis. While multiple algorithms were proposed for full enumeration or sampling-based estimates, these methods fail in very large graphs. Recent advances in parallelization allow for estimates of total sub-graphs counts in very large graphs. The task of counting the frequency of each sub-graph associated with each vertex also received excellent solutions for undirected graphs. However, there is currently no good solution for very large directed graphs. We here propose VDMC (Vertex specific Distributed Motif Counting) -- a fully distributed algorithm to optimally count all the 3 and 4 vertices connected directed graphs (sub-graph motifs) associated with each vertex of a graph. VDMC counts each motif only once and its efficacy is linear in the number of counted motifs. It is fully parallelized to be efficient in GPU-based computation. VDMC is based on three main elements: 1) Ordering the vertices and only counting motifs containing increasing order vertices, 2) sub-ordering motifs based on the average length of the BFS composing the motif, and 3) removing isomorphisms only once for the entire graph. We here compare VDMC to analytical estimates of the expected number of motifs and show its accuracy. VDMC is available as a highly efficient CPU and GPU code with a novel data structure for efficient graph manipulation. We show the efficacy of VDMC and real-world graphs. VDMC allows for the precise analysis of sub-graph frequency around each vertex in large graphs and opens the way for the extension of methods until now limited to graphs of thousands of edges to graphs with millions of edges and above. GIT: https://github.com/louzounlab/graph-measures
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