Neighborhood broadcasting in undirected de Brulin and Kautz networks

This paper considers a neighborhood broadcasting protocol in undirected de Bruijn and Kautz networks. The neighborhood broadcasting problem(NBP) is the problem of disseminating a message from an originator vertex to only its neighbors. Our protocol works under the single-port and half-duplex model and solves NBP in 5 log(2)(n + 1) + O(1) time units on the undirected. de Bruijn graph UB(n, d) with n(d) vertices and the undirected Kautz graph UK(n, d) with n(d)+n(d-1) vertices, where 2n is the maximum degree of these graphs. This completion time is asymptotically optimal in this model.