Improved Algorithms for Approximate String Matching (Extended Abstract)

TL;DR

This paper introduces a new output-sensitive algorithm for approximate string matching that improves theoretical bounds and performs well in practice, especially for strings with significant length differences.

Contribution

The paper presents a novel output-sensitive algorithm for edit distance with improved theoretical bounds and practical performance.

Findings

Achieves time complexity O((s-|n-m|)min(m,n,s)+m+n)

Outperforms existing algorithms in cases with large length differences

Source code is publicly available for implementation and testing.

Abstract

The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share. We designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s-|n-m|)min(m,n,s)+m+n) and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm excels also in practice, especially in cases where the two strings compared differ significantly in length. Source code of our algorithm is available at http://www.cs.miami.edu/\~dimitris/edit_distance