Theoretical analysis of edit distance algorithms: an applied perspective

TL;DR

This paper systematically reviews various theoretical analysis techniques applied to edit distance algorithms, assessing their success in predicting empirical performance and guiding practical algorithm design.

Contribution

It provides a comprehensive survey of theoretical analysis methods for edit distance and evaluates their effectiveness in practical algorithm development.

Findings

Two widely used algorithms are well-predicted by theory.

Most theoretically developed algorithms lack practical relevance.

The analysis techniques have mixed success in achieving their goals.

Abstract

Given its status as a classic problem and its importance to both theoreticians and practitioners, edit distance provides an excellent lens through which to understand how the theoretical analysis of algorithms impacts practical implementations. From an applied perspective, the goals of theoretical analysis are to predict the empirical performance of an algorithm and to serve as a yardstick to design novel algorithms that perform well in practice. In this paper, we systematically survey the types of theoretical analysis techniques that have been applied to edit distance and evaluate the extent to which each one has achieved these two goals. These techniques include traditional worst-case analysis, worst-case analysis parametrized by edit distance or entropy or compressibility, average-case analysis, semi-random models, and advice-based models. We find that the track record is mixed. On one hand, two algorithms widely used in practice have been born out of theoretical analysis and their empirical performance is captured well by theoretical predictions. On the other hand, all the algorithms developed using theoretical analysis as a yardstick since then have not had any practical relevance. We conclude by discussing the remaining open problems and how they can be tackled.