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

TL;DR

This paper presents a near-optimal algorithm with O(n^2) time complexity for calculating the exact Dynamic Time Warping distance between run-length encoded strings, improving upon previous methods and matching known lower bounds.

Contribution

The paper introduces the first O(n^2) time exact algorithm for DTW on run-length encoded strings, achieving near-optimal performance.

Findings

Achieves O(n^2) time complexity for DTW on run-length encoded strings

Matches the conditional lower bound for the problem

Improves upon previous O(n^3) exact algorithm

Abstract

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.