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arXiv · 2509.23326

Finding the diameter of a tree with distance queries

Dániel Gerbner·András Imolay·Kartal Nagy·Balázs Patkós·Kristóf Zólomy
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Abstract

We study the number of distance queries needed to identify certain properties of a hidden tree $T$ on $n$ vertices. A distance query consists of two vertices $x,y$, and the answer is the distance of $x$ and $y$ in $T$. We determine the number of queries an optimal adaptive algorithm needs to find two vertices of maximal distance up to an additive constant, and the number of queries needed to identify the hidden tree asymptotically. We also study the non-adaptive versions of these problems, determining the number of queries needed exactly.

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Dániel Gerbner, András Imolay, Kartal Nagy, Balázs Patkós, Kristóf Zólomy. 2025-09-27. Finding the diameter of a tree with distance queries. https://arxiv.org/abs/2509.23326

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