Balázs Patkós, Alfréd Rényi Institute of Mathematics

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 of at most 5, 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.

Joint work with Dániel Gerbner, András Imolay, Kartal Nagy, and Kristóf Zólomy.