Comment by necessity

The Wagner-Fischer (1970) algorithm they mention (AKA Needleman-Wunsch, Lowrance-Wagner, etc) is quadratic in time and space. It might never get any better than that in time - an improved version with linear space complexity was presented by Hirschberg in 75 - but that doesn't mean execution times can't be improved. Today there are various variations of the same family of algorithms with ever improving execution times. Some adapt the algorithm to massively parallel setups with hundreds of GPUs, others use speculative execution, some use approximations, and so forth.