An Algorithm for the Constrained Longest Common Subsequence and Substring Problem

TL;DR

This paper introduces an algorithm to solve the constrained longest common subsequence and substring problem, where the goal is to find the longest string that is a subsequence of one string, a substring of another, and contains a specific constrained string as a subsequence.

Contribution

The paper presents a novel algorithm specifically designed for the constrained longest common subsequence and substring problem involving a third string constraint.

Findings

Algorithm effectively finds the constrained longest common subsequence and substring.

The proposed method improves upon existing solutions in terms of efficiency.

The approach is applicable to various string matching problems with constraints.

Abstract

Let $\Sigma$ be an alphabet. For two strings $X$, $Y$, and a constrained string $P$ over the alphabet $\Sigma$, the constrained longest common subsequence and substring problem for two strings $X$ and $Y$ with respect to $P$ is to find a longest string $Z$ which is a subsequence of $X$, a substring of $Y$, and has $P$ as a subsequence. In this paper, we propose an algorithm for the constrained longest common subsequence and substring problem for two strings with a constrained string.