论文标题

AOT:推动主机三角列表的效率边界

AOT: Pushing the Efficiency Boundary of Main-memory Triangle Listing

论文作者

Yu, Michael, Qin, Lu, Zhang, Ying, Zhang, Wenjie, Lin, Xuemin

论文摘要

在许多实际应用中,三角列表是重要的主题。三角列表的任务存在有效的算法。最近的算法利用了方向框架,可以将其视为将无向图映射到有向的链接图,即相对于任何全局顶点顺序,即定向图。在本文中,我们提出了一种满足方向技术的自适应取向技术,但在计算三角形计算过程中根据方向图中的顶点仔细仔细遍历它来完善它。基于这种自适应取向技术,我们设计了一种新算法,即AOT,以增强边缘插图列表范式。我们还通过在顶点的相邻列表中利用本地顺序来改进AOT的性能。 我们表明,AOT是第一批可以在实际绩效和理论时间复杂性方面达到最佳性能的工作。我们的全面实验超过$ 16 $真实的大图显示了与最先进的算法相比,我们的\ aot算法的表现出色,尤其是对于数十亿个边缘的大型图表。从理论上讲,我们表明我们提出的算法的时间复杂性为$θ(\ sum_ {\ langle u,v \ rangle \ in \ vec {e}}} \ min \ min \ min \ min \ {deg^{+} {+} {+} {+}(u) $ deg^{+}(x)$分别在定向图和顶点$ x $的外观中表示有向边的集合。至于我们的最佳知识,这是内存三角列表算法中最好的时间复杂性。

Triangle listing is an important topic significant in many practical applications. Efficient algorithms exist for the task of triangle listing. Recent algorithms leverage an orientation framework, which can be thought of as mapping an undirected graph to a directed acylic graph, namely oriented graph, with respect to any global vertex order. In this paper, we propose an adaptive orientation technique that satisfies the orientation technique but refines it by traversing carefully based on the out-degree of the vertices in the oriented graph during the computation of triangles. Based on this adaptive orientation technique, we design a new algorithm, namely aot, to enhance the edge-iterator listing paradigm. We also make improvements to the performance of aot by exploiting the local order within the adjacent list of the vertices. We show that aot is the first work which can achieve best performance in terms of both practical performance and theoretical time complexity. Our comprehensive experiments over $16$ real-life large graphs show a superior performance of our \aot algorithm when compared against the state-of-the-art, especially for massive graphs with billions of edges. Theoretically, we show that our proposed algorithm has a time complexity of $Θ(\sum_{ \langle u,v \rangle \in \vec{E} } \min\{ deg^{+}(u),deg^{+}(v)\}))$, where $\vec{E}$ and $deg^{+}(x)$ denote the set of directed edges in an oriented graph and the out-degree of vertex $x$ respectively. As to our best knowledge, this is the best time complexity among in-memory triangle listing algorithms.

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