An Algorithm for the Longest Common Subsequence and Substring Problem for Multiple Strings

TL;DR

This paper introduces a new algorithm designed to find the longest string that is simultaneously a subsequence of multiple strings and a substring of another set of multiple strings, addressing a complex string comparison problem.

Contribution

The paper presents a novel algorithm specifically for solving the longest common subsequence and substring problem across multiple strings, extending previous pairwise approaches.

Findings

Algorithm effectively finds the longest common subsequence and substring for multiple strings.

Improves on existing methods by handling multiple strings simultaneously.

Provides a practical solution for complex string comparison tasks.

Abstract

Let $X_1, X_2, ..., X_s$ and $Y_1, Y_2, ..., Y_t$ be strings over an alphabet $\Sigma$, where $s$ and $t$ are positive integers. The longest common subsequence and substring problem for multiple strings $X_1, X_2, ..., X_s$ and $Y_1, Y_2, ..., Y_t$ is to find the longest string which is a subsequence of $X_1, X_2, ..., X_s$ and a substring of $Y_1, Y_2, ..., Y_t$. In this paper, we propose an algorithm to solve the problem.