Learning Hypertrees From Shortest Path Queries

We consider the problem of learning a labeled hypergraph from a given family of hypergraphs, using shortest path (SP) queries. An SP query specifies two vertices and asks for their distance in the target hypergraph. For various classes $\mathcal{H}$ of hypertrees, we present bounds on the number of queries required to learn an unknown hypertree from $\mathcal{H}$. Matching upper and lower asymptotic bounds are presented for learning hyperpaths and hyperstars, both in the adaptive and in the non-adaptive setting. Moreover, two non-trivial classes of hypertrees are shown to be efficiently learnable from adaptive SP queries, under certain conditions on structural parameters.