Longest common subsequences in sets of words

TL;DR

This paper establishes a lower bound on the length of the longest common subsequence among a set of words, showing it depends on the alphabet size, word length, and the number of words, with the bound being nearly optimal.

Contribution

It provides a new theoretical lower bound for the longest common subsequence in multiple words, extending previous results and demonstrating sharpness up to a constant factor.

Findings

Lower bound on common subsequence length depending on parameters

Bound is sharp up to a constant factor

Results apply to words over a finite alphabet

Abstract

Given a set of $t$ words of length $n$ over a $k$-letter alphabet, it is proved that there exists a common subsequence among two of them of length at least $\frac{n}{k}+cn^{1-1/(t-k-2)}$, for some $c>0$ depending on $k$ and $t$. This is sharp up to the value of $c$.