Ω(D log(N/D)) lower bound for broadcast in radio networks

Abstract

We show that for any randomized broadcast protocol for radio networks, there exists a network in which the expected time to broadcast a message is Ω(D log(N/D)), where D is the diameter of the network and N is the number of nodes. This implies a tight lower bound of Ω(D log N) for all D≤N1-ε, where ε>0 is any constant.