Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time, and hence the road network can be modeled as a time-dependent graph. In this paper, we study the shortest path query over large-scale time-dependent road networks. Existing work focuses on a hierarchical partition structure, which makes the index construction and travel cost query inefficient. To improve the efficiency of such queries, we propose a novel index by decomposing a road network into a tree structure and selecting a set of shortcuts on the tree to speed up the query processing. Specifically, we first formally define a shortcut selection problem over the tree decomposition of the time-dependent road network. This problem, which is proven to be NP-hard, aims to select and build the most effective shortcut set. We first devise a dynamic programming method with exact results to solve the selection problem. To obtain the optimal shortcut set quickly, we design an approximation algorithm that guarantees a 0.5-approximation ratio. Based on the novel tree structure, we devise a shortcut-based algorithm to answer the shortest path query over time-dependent road networks. Finally, we conduct extensive performance studies using large-scale real-world road networks. The results demonstrate that our method can achieve better efficiency and scalability than the state-of-the-art method.

翻译：查询两个顶点之间的最短路径是多种应用中的基本操作，已在静态路网上得到广泛研究。然而现实中，路段的通行成本随时间变化，因此路网可建模为时变图。本文研究大规模时变路网上的最短路径查询问题。现有工作侧重于分层分区结构，导致索引构建和通行成本查询效率低下。为提升此类查询效率，我们提出一种新型索引：将路网分解为树形结构，并选取树上的若干捷径以加速查询处理。具体而言，我们首先正式定义了时变路网树分解上的捷径选取问题。该问题被证明为NP难问题，旨在选取并构建最有效的捷径集。我们首先设计了一种精确结果的动态规划方法来解决选取问题。为快速获取最优捷径集，我们设计了一种保障0.5近似比的近似算法。基于新型树结构，我们提出基于捷径的算法来回答时变路网上的最短路径查询。最后，利用大规模真实路网进行广泛性能研究，结果表明该方法在效率和可扩展性上均优于现有最优方法。