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错位而成为时间序列相似性搜索的基础。这些度量本质上计算代价高昂，因此需要使用下界来剪枝不必要的比较。本文提出了一种新的\emph{二分图边覆盖范式}用于推导下界，该范式适用于广泛的弹性相似性度量类别。该范式将下界计算表述为从输入时间序列导出的加权二分图上的顶点加权问题。在此范式下，现有的大多数弹性相似性度量下界均可视为简单的实例化。我们进一步提出了\textit{BGLB}，作为该范式的一个实例化方法，它引入了一个额外的增强项，从而产生可证明更紧的下界。在128个真实世界数据集上的理论分析和广泛实验表明，\textit{BGLB} 为六种弹性度量（ERP、MSM、TWED、LCSS、EDR和SWALE）实现了已知最紧的下界。此外，\textit{BGLB} 在\textit{DTW} 度量上仍保持高度竞争力，在紧致性和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现有最先进方法，在各种弹性相似性度量上实现了$24.6\%$到$84.9\%$的加速比。此外，\textit{BGLB} 在基于密度的聚类应用中也实现了显著加速，验证了\textit{BGLB} 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。