An Algorithm for the Longest Common Subsequence and Substring Problem

TL;DR

This paper introduces a new problem combining longest common subsequence and substring concepts and proposes an algorithm to solve it, expanding the scope of string similarity measures.

Contribution

The paper defines a novel problem and provides an algorithmic solution, advancing methods for string comparison tasks.

Findings

Proposed an algorithm for the combined longest common subsequence and substring problem.

Established the problem's formal definition and scope.

Demonstrated the algorithm's effectiveness in solving the new problem.

Abstract

In this note, we first introduce a new problem called the longest common subsequence and substring problem. Let $X$ and $Y$ be two strings over an alphabet $\Sigma$. The longest common subsequence and substring problem for $X$ and $Y$ is to find the longest string which is a subsequence of $X$ and a substring of $Y$. We propose an algorithm to solve the problem.