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:双向搜索是一种在图中加快最短路径查询速度的常见技术,即从起点进行前向搜索,从目的地进行后向搜索,直到找到一条最短路径上的公共节点。实际上,这对于某些现实世界网络的性能有着巨大的影响,而在其他类型的网络上似乎只能节省一定的常数因子。虽然寻找最短路径是一种普遍存在的问题,但只有很少的研究试图通过对某些现实世界网络模型的平均情况分析来理解这些网络上的渐近加速。在本文中,我们通过分析可以在任何特定实例上进行有效检验的确定性属性,给出了一个新的视角,这些属性允许理论分析,并且在几个区域内证明了这些参数意味着双向广度优先搜索的次线性运行时间,其中一些是紧的。此外,我们在大量的现实世界网络上进行实验,表明我们的参数很好地捕捉了实际运行时间的概念。