A Fast Randomized Algorithm for Finding the Maximal Common Subsequences

TL;DR

This paper introduces a fast randomized algorithm called Random-MCS for finding maximal common subsequences among multiple strings, which is efficient for large numbers of strings and often approximates the longest common subsequence.

Contribution

The paper presents a novel randomized algorithm for Maximal Common Subsequence that operates in linear time relative to the number of strings, suitable for large-scale problems.

Findings

Algorithm complexity is linear in the number of strings.

Repeated runs often yield solutions close to the LCS.

Theoretical and experimental validation of the approach.

Abstract

Finding the common subsequences of $L$ multiple strings has many applications in the area of bioinformatics, computational linguistics, and information retrieval. A well-known result states that finding a Longest Common Subsequence (LCS) for $L$ strings is NP-hard, e.g., the computational complexity is exponential in $L$. In this paper, we develop a randomized algorithm, referred to as {\em Random-MCS}, for finding a random instance of Maximal Common Subsequence ($MCS$) of multiple strings. A common subsequence is {\em maximal} if inserting any character into the subsequence no longer yields a common subsequence. A special case of MCS is LCS where the length is the longest. We show the complexity of our algorithm is linear in $L$, and therefore is suitable for large $L$. Furthermore, we study the occurrence probability for a single instance of MCS and demonstrate via both theoretical and experimental studies that the longest subsequence from multiple runs of {\em Random-MCS} often yields a solution to $LCS$.