Centralized broadcast in multihop radio networks

We show that for any radio network there exists a schedule of a broadcast whose time is O(D+log⁵ n), where D is the diameter and n is the number of nodes. (This result implies an optimal broadcast to networks with D = Ω(log⁵ n).) We present a centralized randomized polynomial time algorithm that given a network and a source, outputs a schedule for broadcasting the message from the source to the rest of the network.