Near-Optimal Dynamic Time Warping on Run-Length Encoded Strings

We give an $\tilde O(n^2)$ time algorithm for computing the exact Dynamic Time Warping distance between two strings whose run-length encoding is of size at most $n$. This matches (up to log factors) the known (conditional) lower bound, and should be compared with the previous fastest $O(n^3)$ time exact algorithm and the $\tilde O(n^2)$ time approximation algorithm.