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arXiv · 2504.10425

Expected Length of the Longest Common Subsequence of Multiple Strings

Ray Li·William Ren·Yiran Wen
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Abstract

We study the generalized Chvátal-Sankoff constant $γ_{k,d}$, which represents the normalized expected length of the longest common subsequence (LCS) of $d$ independent uniformly random strings over an alphabet of size $k$. We derive asymptotically tight bounds for $γ_{2,d}$, establishing that $γ_{2,d} = \frac{1}{2} + Θ\left(\frac{1}{\sqrt{d}}\right)$. We also derive asymptotically near-optimal bounds on $γ_{k,d}$ for $d\ge Ω(\log k)$.

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Ray Li, William Ren, Yiran Wen. 2025-04-14. Expected Length of the Longest Common Subsequence of Multiple Strings. https://arxiv.org/abs/2504.10425

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