Average-Case Optimal Approximate Circular String Matching

TL;DR

This paper introduces a new algorithm for approximate circular string matching that achieves optimal average-case search time under the edit distance model, improving efficiency over previous methods.

Contribution

The paper presents a novel algorithm for approximate circular string matching with optimal average-case complexity and reduced preprocessing time and space requirements.

Findings

Achieves average-case search time of O(n(k + log m)/m)

Reduces preprocessing time and space compared to multiple pattern matching methods

Provides an efficient solution for approximate circular string matching under edit distance

Abstract

Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that are at a distance at most k from x or from any of its rotations. In this article, we present a new algorithm for approximate circular string matching under the edit distance model with optimal average-case search time O(n(k + log m)/m). Optimal average-case search time can also be achieved by the algorithms for multiple approximate string matching (Fredriksson and Navarro, 2004) using x and its rotations as the set of multiple patterns. Here we reduce the preprocessing time and space requirements compared to that approach.