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Pré-Publication, Document De Travail Année : 2022

An Improved Lower Bound on the Largest Common Subtree of Random Leaf-Labeled Binary Trees

Résumé

It is known that the size of the largest common subtree (i.e., the maximum agreement subtree) of two independent random binary trees with $n$ given labeled leaves is of order between $n^{0.366}$ and $n^{1/2}$. We improve the lower bound to order $n^{0.4464}$ by constructing a common subtree recursively and by proving a lower bound for its asymptotic growth. The construction is a modification of an algorithm proposed by D. Aldous by splitting the tree at the centroid and by proceeding recursively.

Dates et versions

hal-03924930 , version 1 (05-01-2023)

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Ali Khezeli. An Improved Lower Bound on the Largest Common Subtree of Random Leaf-Labeled Binary Trees. 2022. ⟨hal-03924930⟩
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