# Quasi-Linear-Time Algorithm for Longest Common Circular Factor

## TL;DR

This paper presents a novel algorithm that efficiently computes the longest common circular factor between two strings, extending the classic longest common factor problem with a cyclic shift consideration, in near-linear time.

## Contribution

The paper introduces the LCCF problem and provides the first quasi-linear time algorithm to solve it, advancing string similarity measures.

## Key findings

- LCCF can be computed in O(n log^5 n) time.
- The algorithm extends classic string matching techniques.
- LCCF serves as a new similarity measure for strings.

## Abstract

We introduce the Longest Common Circular Factor (LCCF) problem in which, given strings $S$ and $T$ of length $n$, we are to compute the longest factor of $S$ whose cyclic shift occurs as a factor of $T$. It is a new similarity measure, an extension of the classic Longest Common Factor. We show how to solve the LCCF problem in $O(n \log^5 n)$ time.