Computing the Number of Longest Common Subsequences

TL;DR

This paper introduces simple and efficient algorithms to compute the number of distinct longest common subsequences and their embeddings for two input strings, improving understanding of sequence similarity.

Contribution

It presents novel algorithms for counting the number of LCS and LCS embeddings, which were not previously available in such simple forms.

Findings

Algorithms are efficient and straightforward

They accurately count the number of LCS and embeddings

Potential applications in sequence analysis and bioinformatics

Abstract

This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.