Algorithms for the uniqueness of the longest common subsequence

TL;DR

This paper introduces algorithms to determine the uniqueness of the longest common subsequence across various sequence types, with applications in bioinformatics and gene sequencing.

Contribution

It presents novel algorithms for assessing the uniqueness of LCS in linear and circular sequences, including cases with duplicated numbers.

Findings

Algorithms successfully determine LCS uniqueness.

Applications demonstrated on gene sequencing data.

Different sequence scenarios are effectively handled.

Abstract

Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works only consider how to find one longest common subsequence. In this paper, we consider how to determine the uniqueness of the longest common subsequence. If there are multiple longest common subsequences, we also determine which number appears in all/some/none of the longest common subsequences. We focus on four scenarios: (1) linear sequences without duplicated numbers; (2) circular sequences without duplicated numbers; (3) linear sequences with duplicated numbers; (4) circular sequences with duplicated numbers. We develop corresponding algorithms and apply them to gene sequencing data.