Tight lower bounds for Dynamic Time Warping

Geoffrey I. Webb, François Petitjean

Research output: Contribution to journalArticleResearchpeer-review


Dynamic Time Warping (DTW) is a popular similarity measure for aligning and comparing time series. Due to 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. LB_KEOGH provides a useful trade-off in many applications. Two recent lower bounds, LB_IMPROVED and LB_ENHANCED, are substantially tighter than LB_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 DTW lower bounds in the same complexity class. LB_PETITJEAN is substantially tighter than LB_IMPROVED, with only modest additional computational overhead. LB_WEBB is more efficient than LB_IMPROVED, while often providing a tighter bound. LB_WEBB is always tighter than LB_KEOGH. The parameter free LB_WEBB is usually tighter than LB_ENHANCED. A parameterized variant, LB_WEBB_ENHANCED, is always tighter than LB_ENHANCED. A further variant, LB_WEBB*, is useful for some constrained distance functions. In extensive experiments, LB_WEBB proves to be very effective for nearest neighbor search.

Original languageEnglish
Article number107895
Number of pages12
JournalPattern Recognition
Publication statusPublished - Jul 2021


  • Dynamic time warping
  • Lower bound
  • Time series

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