Elastic similarity measures are fundamental to time series similarity search because of their ability to handle temporal misalignments. These measures are inherently computationally expensive, therefore necessitating the use of lower bounds to prune unnecessary comparisons. This paper proposes a new \emph{Bipartite Graph Edge-Cover Paradigm} for deriving lower bounds, which applies to a broad class of elastic similarity measures. This paradigm formulates lower bounding as a vertex-weighting problem on a weighted bipartite graph induced from the input time series. Under this paradigm, most of the existing lower bounds of elastic similarity measures can be viewed as simple instantiations. We further propose \textit{BGLB}, an instantiation of the proposed paradigm that incorporates an additional augmentation term, yielding lower bounds that are provably tighter. Theoretical analysis and extensive experiments on 128 real-world datasets demonstrate that \textit{BGLB} achieves the tightest known lower bounds for six elastic measures (ERP, MSM, TWED, LCSS, EDR, and SWALE). Moreover, \textit{BGLB} remains highly competitive for \textit{DTW} with a favorable trade-off between tightness and computational efficiency. In nearest neighbor search, integrating \textit{BGLB} into filter pipelines consistently outperforms state-of-the-art methods, achieving speedups ranging from $24.6\%$ to $84.9\%$ across various elastic similarity measures. Besides, \textit{BGLB} also delivers a significant acceleration in density-based clustering applications, validating the practical potential of \textit{BGLB} in time series similarity search tasks based on elastic similarity measures.

翻译：弹性相似性度量因其能够处理时间序列中的时间错位问题而成为时间序列相似性搜索的基础。这些度量本质上是计算昂贵的，因此需要利用下界来剪除不必要的比较。本文提出了一种新的\textit{二分图边覆盖框架}用于推导下界，该框架适用于广泛的弹性相似性度量。该框架将下界问题形式化为一个基于输入时间序列诱导的加权二分图上的顶点加权问题。在此框架下，现有的大多数弹性相似性度量下界可被视为简单的实例化。我们进一步提出了\textit{BGLB}，这是所提框架的一种实例化，通过引入额外的增广项，得到了理论上更紧的下界。理论分析及在128个真实数据集上的大量实验表明，对于六种弹性度量（ERP、MSM、TWED、LCSS、EDR和SWALE），\textit{BGLB}实现了已知最紧的下界。此外，\textit{BGLB}在\textit{DTW}上也极具竞争力，在紧致性与计算效率之间取得了良好平衡。在最近邻搜索中，将\textit{BGLB}集成到过滤流水线中始终优于最先进的方法，对于各种弹性相似性度量，加速比达到$24.6\%$至$84.9\%$。此外，\textit{BGLB}在基于密度的聚类应用中同样实现了显著加速，验证了其在基于弹性相似性度量的时间序列相似性搜索任务中的实际潜力。