Optimal Gossiping with Unit Size Messages in Known Topology Radio Networks

Gossiping is a communication primitive where each node of a network possesses a unique message that is to be communicated to all other nodes in the network. We study the gossiping problem in known topology radio networks where the schedule of transmissions is precomputed in advance based on full knowledge about the size and the topology of the network. In addition we consider the case where it is only possible to transmit a unit size message in each time step. This gives a more realistic model than if arbitrary length messages can be sent during each time step, as has been the case in most previous studies of the gossiping problem. In this paper, we propose an optimal randomized schedule that uses O(n log n) time units to complete the gossiping task with high probability in any radio network of size n. This matches the lower bound of Ω(n log n) by Gąsieniec and Potapov in [17] [TCS’02]. Our new gossiping schedule is based on the notion of a gathering spanning tree proposed by Gąsieniec, Peleg and Xin in [19] [PODC’05].