Dynamic time warping (DTW) is a fundamental technique in time series analysis for comparing one curve to another using a flexible time-warping function. However, it was designed to compare a single pair of curves. In many applications, such as in metabolomics and image series analysis, alignment is simultaneously needed for multiple pairs. Because the underlying warping functions are often related, independent application of DTW to each pair is a sub-optimal solution. Yet, it is largely unknown how to efficiently conduct a joint alignment with all warping functions simultaneously considered, since any given warping function is constrained by the others and dynamic programming cannot be applied.

Technical quality: The discussion of the proofs in the paper is very brief, making the technical sections quite dense. The supplemental material fills in the details and the proofs appear to be correct. One issue that could be addressed more clearly in the paper and the supplemental is the need for infinite weight reverse edges in the dual graph. This is currently not explained at all in the main paper other than stating these edges are important and later empirically demonstrating that not including them leads to violations of DTW warping constraints. The hyper-parameter tuning section was very brief and the algorithm is not clear.

Dynamic time warping (DTW) is a fundamental technique in time series analysis for comparing one curve to another using a flexible time-warping function. However, it was designed to compare a single pair of curves. In many applications, such as in metabolomics and image series analysis, alignment is simultaneously needed for multiple pairs. Because the underlying warping functions are often related, independent application of DTW to each pair is a sub-optimal solution. Yet, it is largely unknown how to efficiently conduct a joint alignment with all warping functions simultaneously considered, since any given warping function is constrained by the others and dynamic programming cannot be applied.