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

TL;DR

The longest common subsequence and substring problem for multiple strings X1, X2, ..., Xs and Y1, Y2, ..., Yt is to find the longest string which is a subsequence of X1, X2, ..., Xs and a substring of Y1, Y2, ..., Yt.

Abstract

Let $X_1, X_2, ..., X_s$ and $Y_1, Y_2, ..., Y_t$ be strings over an alphabet $Σ$, 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.