An $O(n^2)$ Algorithm for Computing Longest Common Cyclic Subsequence

TL;DR

This paper introduces an efficient $O(n^2)$ algorithm for computing the longest common cyclic subsequence, a problem relevant in biological sequence analysis involving circular DNA and RNA.

Contribution

The paper presents the first quadratic-time algorithm for the LCCS problem, extending classical LCS to circular sequences.

Findings

The algorithm runs in $O(n^2)$ time.

It effectively handles all circular shifts of strings.

Applicable in biological sequence comparison.

Abstract

The {\em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. LCS is a central problem in stringology and finds broad applications in text compression, error-detecting codes and biological sequence comparison. However, in numerous contexts, words represent cyclic sequences of symbols and LCS must be generalized to consider all circular shifts of the strings. This occurs especially in computational biology when genetic material is sequenced form circular DNA or RNA molecules. This initiates the problem of {\em longest common cyclic subsequence (LCCS)} which finds the longest subsequence between all circular shifts of two strings. In this paper, we give an $O(n^2)$ algorithm for solving LCCS problem where $n$ is the number of symbols in the strings.