Many Flavors of Edit Distance

TL;DR

This paper explores the relationships between different string similarity measures, demonstrating how to reduce complex problems over large alphabets to simpler binary cases and transforming indel distance questions into edit distance ones.

Contribution

It provides methods to reduce string similarity problems over arbitrary alphabets to binary alphabets and transforms indel distance questions into edit distance questions.

Findings

Reduction of string similarity problems to binary alphabet cases.

Transformation of indel distance questions into edit distance questions.

Complementing earlier results by Tiskin (2007).

Abstract

Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another, while the latter specifically quantifies the number of insertions and deletions. Many algorithmic solutions explicitly address one of these measures, and frequently techniques applicable to one can also be adapted to work with the other. In this paper, we investigate whether there exists a standardized approach for applying results from one setting to another. Specifically, we demonstrate the capability to reduce questions regarding string similarity over arbitrary alphabets to equivalent questions over a binary alphabet. Furthermore, we illustrate how to transform questions concerning indel distance into equivalent questions based on edit distance. This complements an earlier result of Tiskin (2007) which addresses the inverse direction.