Reconstructing a Bounded-Degree Directed Tree Using Path Queries [article]

Zhaosen Wang, Jean Honorio
2017 arXiv   pre-print
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^2 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. Regarding lower bounds, we show that any randomized algorithm requires at least Ω(n n) queries, while any deterministic algorithm requires at least Ω(dn) queries. Additionally, we present a O(dn^3 n)
more » ... omized algorithm for noisy queries, and a O(dn^2 n) randomized algorithm for additive queries on weighted trees.
arXiv:1606.05183v3 fatcat:thzx62zvcfaszceuf5l25zedhe