Lower bounds for the broadcast problem in mobile radio networks

In this paper, we prove a lower bound on the number of rounds required by a deterministic distributed protocol for broadcasting a message in radio networks whose processors do not know the identities of their neighbors. Such an assumption captures the main characteristic of mobile and wireless environments [3], i.e., the instability of the network topology. For any distributed broadcast protocol Pi, for any n and for any D less than or equal to n/2, we exhibit a network G with n nodes and diameter D such that the number of rounds needed by Pi for broadcasting a message in G is Omega(D log n). The result still holds even if the processors in the network use a different program and know n and D. We also consider the version of the broadcast problem in which an arbitrary number of processors issue at the same time an identical message that has to be delivered to the other processors. In such a case we prove that, even assuming that the processors know the network topology, Omega(n) rounds are required for solving the problem on a complete network (D = 1) with n processors.