Reconstructing a Bounded-Degree Directed Tree Using Path Queries

We present a randomized algorithm for reconstructing directed rooted trees of n nodes and node degree at most d, by asking at most O(dn log n) path queries. Each path query takes as input an origin node and a target node, and answers whether there is a directed path from the origin to the target. Our algorithm is only a factor of O(d log n) from the informationtheoretic lower bound of Ω(n log n) for any deterministic or randomized algorithm. We also present a O(dn log n) randomized algorithm for noisy queries, and a O(dn log n) randomized algorithm for additive queries on weighted trees.