Time series indexing plays an important role in querying and pattern mining of big data. This paper proposes a novel structure for tightly covering a given set of time series under the dynamic time warping similarity measurement. The structure, referred to as dynamic covering with cross-range constraints (DCRC), enables more efficient and scalable indexing to be developed than current hypercube-based partitioning approaches. In particular, a lower bound of the DTW distance from a given query time series to a DCRC-based cover set is introduced. By virtue of its tightness, which is proven theoretically, the lower bound can be used for pruning when querying on an indexing tree. If the DCRC-based lower bound (LB_DCRC) of an upper node in an index tree is larger than a given threshold, all child nodes can be pruned yielding a significant reduction in computational time. A hierarchical DCRC (HDCRC) structure is proposed to generate the DCRC-tree-based indexing and used to develop time series indexing and insertion algorithms. Experimental results for a selection of benchmark time series datasets are presented to illustrate the tightness of LB_DCRC, as well as the pruning efficiency on the DCRC-tree, especially when the time series have large deformations.

时间序列索引在大数据的查询和模式挖掘中起着重要作用。本文提出了一种新颖的结构，用于在动态时间规整相似性度量下紧密覆盖给定的时间序列集。该结构被称为具有跨范围约束的动态覆盖（DCRC），与当前基于超多维数据集的分区方法相比，它可以开发出更高效和可扩展的索引。特别是，介绍了从给定查询时间序列到基于DCRC的覆盖集的DTW距离的下限。凭借其紧密性（已在理论上得到证明），在对索引树进行查询时，下限可用于修剪。如果索引树中上层节点的基于DCRC的下限（LB_DCRC）大于给定阈值，可以修剪所有子节点，从而显着减少计算时间。提出了一种分层的DCRC（HDCRC）结构来生成基于DCRC树的索引，并用于开发时间序列索引和插入算法。给出了一些基准时间序列数据集的实验结果，以说明LB_DCRC的紧密性以及DCRC树上的修剪效率，尤其是在时间序列变形较大时。