This article studies the core maintenance problem for dynamic graphs which requires to update each vertex's core number with the insertion/deletion of vertices/edges. Previous algorithms can either process one edge associated with a vertex in each iteration or can only process one superior edge associated with the vertex (an edge $\langle u,v\rangle$〈u,v〉 is a superior edge of vertex $u$u if $v$v’ core number is no less than $u$u's core number) in each iteration. Thus for high superior-degree vertices (the vertices associated with many superior edges) insertions/deletions, previous algorithms become very inefficient. In this article, we discovered a new structure called joint edge set whose insertions/deletions make each vertex's core number change at most one. The joint edge set mainly contains all the superior edges associated with the high superior-degree vertices as long as these vertices are 3$^+$+-hop independent. Based on this discovery, faster parallel algorithms are devised to solve the core maintenance problems. In our algorithms, we can process all edges in the joint edge set in one iteration and thus can greatly increase the parallelism and reduce the processing time. The results of extensive experiments conducted on various types of real-world, temporal, and synthetic graphs illustrate that the proposed algorithms achieve good efficiency, stability and scalability. Specifically, the new algorithms can outperform the single-edge processing algorithms by up to four orders of magnitude. Compared with the matching based algorithm and the superior edge based algorithm, our algorithms show a significant speedup up to 60× in the processing time.

中文翻译：

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动态图中更快的并行核心维护算法

本文研究动态图的核心维护问题，该问题需要通过插入/删除顶点/边来更新每个顶点的核心数。以前的算法可以在每次迭代中处理与顶点关联的一条边，也可以只处理与顶点关联的一条上级边（一条边$\lange u,v\rangle$〈你,v〉 是顶点的上边缘 $u$你 如果 $v$v' 核心数不小于 $u$你的核心数）在每次迭代中。因此，对于高上级顶点（与许多上级边关联的顶点）插入/删除，以前的算法变得非常低效。在这篇文章中，我们发现了一种称为联合边集的新结构，它的插入/删除使每个顶点的核心编号最多改变一个。联合边集主要包含与高优度顶点关联的所有优边，只要这些顶点为3$^+$+-跳跃独立。基于这一发现，设计了更快的并行算法来解决核心维护问题。在我们的算法中，我们可以在一次迭代中处理联合边集中的所有边，从而可以大大提高并行度并减少处理时间。对各种类型的真实世界、时间和合成图进行的大量实验结果表明，所提出的算法具有良好的效率、稳定性和可扩展性。具体来说，新算法的性能可以比单边处理算法高四个数量级。与基于匹配的算法和基于优越边缘的算法相比，我们的算法在处理时间上显示出高达 60 倍的显着加速。