Dynamic Time Warping ($\text{DTW}$) is a popular similarity measure for aligning and comparing time series. Due to $\text{DTW}$’s high computation time, lower bounds are often employed to screen poor matches. Many alternative lower bounds have been proposed, providing a range of different trade-offs between tightness and computational efficiency. $\text{LB}\_\text{KEOGH}$ provides a useful trade-off in many applications. Two recent lower bounds, $\text{LB}\_\text{IMPROVED}$ and $\text{LB}\_\text{ENHANCED},$ are substantially tighter than $\text{LB}\_\text{KEOGH}$. All three have the same worst case computational complexity—linear with respect to series length and constant with respect to window size. We present four new $\text{DTW}$ lower bounds in the same complexity class. $\text{LB}\_\text{PETITJEAN}$ is substantially tighter than $\text{LB}\_\text{IMPROVED},$ with only modest additional computational overhead. $\text{LB}\_\text{WEBB}$ is more efficient than $\text{LB}\_\text{IMPROVED},$ while often providing a tighter bound. $\text{LB}\_\text{WEBB}$ is always tighter than $\text{LB}\_\text{KEOGH}$. The parameter free $\text{LB}\_\text{WEBB}$ is usually tighter than $\text{LB}\_\text{ENHANCED}$. A parameterized variant, LB_Webb_Enhanced, is always tighter than $\text{LB}\_\text{ENHANCED}$. A further variant, $\text{LB}\_{\text{WEBB}}^{*},$ is useful for some constrained distance functions. In extensive experiments, $\text{LB}\_\text{WEBB}$ proves to be very effective for nearest neighbor search.

动态时间规整（$\text{DTW}$）是用于对齐和比较时间序列的一种流行的相似性度量。由于$\text{DTW}$的运算时间长，下限通常用于筛选不匹配的内容。已经提出了许多替代的下限，从而在紧密度和计算效率之间提供了一系列不同的权衡。$\text{磅}\_\text{凯奥}$在许多应用程序中提供了有用的折衷。最近的两个下限，$\text{磅}\_\text{改良的}$ 和 $\text{磅}\_\text{增强}，$ 比 $\text{磅}\_\text{凯奥}$。这三个变量都具有相同的最坏情况的计算复杂性-相对于序列长度是线性的，而相对于窗口大小是恒定的。我们提出了四个新的$\text{DTW}$ 同一复杂度类别中的下界。 $\text{磅}\_\text{佩蒂让}$ 比 $\text{磅}\_\text{改良的}，$ 仅需少量的额外计算开销。 $\text{磅}\_\text{WEBB}$ 比 $\text{磅}\_\text{改良的}，$ 同时通常会提供更严格的界限。 $\text{磅}\_\text{WEBB}$ 总是比 $\text{磅}\_\text{凯奥}$。无参数$\text{磅}\_\text{WEBB}$ 通常比 $\text{磅}\_\text{增强}$。参数化变体LB_Webb_Enhanced总是比$\text{磅}\_\text{增强}$。另一个变体$\text{磅}\_{\text{WEBB}}^{*}，$对于某些约束距离函数很有用。在广泛的实验中$\text{磅}\_\text{WEBB}$ 事实证明，它对于最近邻居搜索非常有效。