Fast broadcasting and gossiping in radio networks

We establish an O(n log/sup 2/n) upper bound on the time for deterministic distributed broadcasting in multi-hop radio networks with unknown topology. This nearly matches the known lower bound of /spl Omega/(n log n). The fastest previously known algorithm for this problem works in time O(n/sup 3/2/). Using our broadcasting algorithm, we develop an O(n/sup 3/2/log/sup 2/n) algorithm for gossiping in the same network model.