Improved Time Warp Edit Distance -- A Parallel Dynamic Program in Linear Memory

TL;DR

This paper introduces a parallelizable, memory-efficient algorithm for Time Warp Edit Distance that significantly accelerates computations using a banded dynamic programming approach on GPUs.

Contribution

It presents a novel linear-memory, massively parallel algorithm for Time Warp Edit Distance leveraging a banded dynamic programming structure.

Findings

Achieves significant speedups on challenging problems.

Requires only linear memory for computations.

Parallelizes the update of diagonal elements in the DP matrix.

Abstract

Edit Distance is a classic family of dynamic programming problems, among which Time Warp Edit Distance refines the problem with the notion of a metric and temporal elasticity. A novel Improved Time Warp Edit Distance algorithm that is both massively parallelizable and requiring only linear storage is presented. This method uses the procession of a three diagonal band to cover the original dynamic program space. Every element of the diagonal update can be computed in parallel. The core method is a feature of the TWED Longest Common Subsequence data dependence and is applicable to dynamic programs that share similar band subproblem structure. The algorithm has been implemented as a CUDA C library with Python bindings. Speedups for challenging problems are phenomenal.