A Formula for the Mean Length of the Longest Common Subsequence

Abstract

The expected value E of the longest common subsequence of letters in two random words is considered as a function of the α = |A| of alphabet and of words lengths m and n. It is assumed that each letter independently appears at any position with equal probability. A simple expression for E(α, m, n) and its empirical proof are presented for fixed α and m + n. High accuracy of the formula in a wide range of values is confirmed by numerical simulations.