We show that for any radio network there exists a schedule of a broadcast whose time is O(D + log 5 n), where D is the diameter and n is the number of nodes. (This result implies an optimal broadcast to networks with D = Ω(log 5 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.
Gaber and Mansour REF showed that for any packet radio network there is a schedule of broadcasting giving time O(D + log 5 n), and that it can be found by a deterministic polynomial algorithm.
Centralized broadcast in multihop radio networks
J. Algorithms
Mathematics Computer Science