Similar subtrajectory search is a finer-grained operator that can better capture the similarities between one query trajectory and a portion of a data trajectory than the traditional similar trajectory search, which requires the two checked trajectories are similar to each other in whole. Many real applications (e.g., trajectory clustering and trajectory join) utilize similar subtrajectory search as a basic operator. It is considered that the time complexity is O(mn^2) for exact algorithms to solve the similar subtrajectory search problem under most trajectory distance functions in the existing studies, where m is the length of the query trajectory and n is the length of the data trajectory. In this paper, to the best of our knowledge, we are the first to propose an exact algorithm to solve the similar subtrajectory search problem in O(mn) time for most of widely used trajectory distance functions (e.g., WED, DTW, ERP, EDR and Frechet distance). Through extensive experiments on three real datasets, we demonstrate the efficiency and effectiveness of our proposed algorithms.

翻译：相似子轨迹搜索是一种比传统相似轨迹搜索更细粒度的操作，能够更好地捕捉查询轨迹与数据轨迹部分片段之间的相似性，而传统相似轨迹搜索要求两条被检轨迹整体相似。许多实际应用（如轨迹聚类和轨迹连接）将相似子轨迹搜索作为基本操作。现有研究表明，在大多数轨迹距离函数下，解决相似子轨迹搜索问题的精确算法时间复杂度为O(mn²)，其中m为查询轨迹长度，n为数据轨迹长度。本文首次提出一种精确算法，在大多数广泛使用的轨迹距离函数（如WED、DTW、ERP、EDR和弗雷歇距离）下，以O(mn)时间复杂度解决相似子轨迹搜索问题。通过在三个真实数据集上的大量实验，我们证明了所提算法的效率和有效性。