A common technique to speed up shortest path queries in graphs is to use a bidirectional search, i.e., performing a forward search from the start and a backward search from the destination until a common vertex on a shortest path is found. In practice, this has a tremendous impact on the performance on some real-world networks, while it only seems to save a constant factor on other types of networks. Even though finding shortest paths is a ubiquitous problem, there are only few studies attempting to understand the apparently asymptotic speedups on some networks, using average case analysis on certain models for real-world networks. In this paper we give a new perspective on this, by analyzing deterministic properties that permit theoretical analysis and that can easily be checked on any particular instance. We prove that these parameters imply sublinear running time for the bidirectional breadth-first search in several regimes, some of which are tight. Moreover, we perform experiments on a large set of real-world networks showing that our parameters capture the concept of practical running time well.

翻译：加速图中最短路径查询的常用技术是采用双向搜索，即从起点执行前向搜索、从终点执行后向搜索，直到找到位于最短路径上的公共顶点。在实践中，该方法对某些现实网络的性能提升极为显著，但在其他类型网络上似乎仅能节省常数因子。尽管最短路径搜索是普遍存在的问题，但仅有少数研究尝试通过针对特定现实网络模型进行平均情况分析，来理解某些网络上呈现的渐近加速现象。本文提出全新视角：通过分析允许理论推导且可在特定实例中轻松检验的确定性性质，证明这些参数在多种场景下（其中部分为紧界）能实现双向广度优先搜索的亚线性运行时间。此外，我们在大量现实网络上开展实验，结果表明所提出的参数能够有效刻画实际运行时间的概念。