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Expected length of the longest common subsequence for large alphabets

Marcos Kiwi·Martin Loebl·Jiri Matousek
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Abstract

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.

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Marcos Kiwi, Martin Loebl, Jiri Matousek. 2003-08-25. Expected length of the longest common subsequence for large alphabets. https://arxiv.org/abs/math/0308234

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