Computing shortest paths is a fundamental operation in processing graph data. In many real-world applications, discovering shortest paths between two vertices empowers us to make full use of the underlying structure to understand how vertices are related in a graph, e.g. the strength of social ties between individuals in a social network. In this paper, we study the shortest-path-graph problem that aims to efficiently compute a shortest path graph containing exactly all shortest paths between any arbitrary pair of vertices on complex networks. Our goal is to design an exact solution that can scale to graphs with millions or billions of vertices and edges. To achieve high scalability, we propose a novel method, Query-by-Sketch (QbS), which efficiently leverages offline labelling (i.e., precomputed labels) to guide online searching through a fast sketching process that summarizes the important structural aspects of shortest paths in answering shortest-path-graph queries. We theoretically prove the correctness of this method and analyze its computational complexity. To empirically verify the efficiency of QbS, we conduct experiments on 12 real-world datasets, among which the largest dataset has 1.7 billion vertices and 7.8 billion edges. The experimental results show that QbS can answer shortest-path graph queries in microseconds for million-scale graphs and less than half a second for billion-scale graphs.

中文翻译：

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素描查询：在超大型网络上扩展最短路径图查询

计算最短路径是处理图形数据的基本操作。在许多实际应用中，发现两个顶点之间的最短路径使我们能够充分利用基础结构来了解图中顶点的关系，例如，社交网络中个体之间的社会纽带的强度。在本文中，我们研究了最短路径图问题，旨在有效地计算最短路径图，其中包含复杂网络上任意任意一对顶点之间的所有最短路径。我们的目标是设计一个精确的解决方案，该解决方案可以缩放到具有数百万或数十亿个顶点和边的图形。为了实现较高的可扩展性，我们提出了一种新颖的方法，即按草图查询（QbS），该方法可以有效利用离线标签（即，预先计算的标签）以指导在线搜索通过一个快速的草图绘制过程，该过程概述了最短路径在回答最短路径图查询中的重要结构方面。我们从理论上证明了该方法的正确性，并分析了其计算复杂性。为了从经验上验证QbS的效率，我们对12个真实世界的数据集进行了实验，其中最大的数据集具有17亿个顶点和78亿个边。实验结果表明，QbS可以以百万分之一秒的速度回答最短路径图查询，而百万亿级的图表则可以不到半秒的时间。为了从经验上验证QbS的效率，我们对12个真实世界的数据集进行了实验，其中最大的数据集具有17亿个顶点和78亿个边。实验结果表明，QbS可以以百万分之一秒的速度回答最短路径图查询，而百万亿级的图表则需要不到半秒的时间。为了从经验上验证QbS的效率，我们对12个真实世界的数据集进行了实验，其中最大的数据集具有17亿个顶点和78亿个边。实验结果表明，QbS可以以百万分之一秒的速度回答最短路径图查询，而百万亿级的图表则需要不到半秒的时间。