Broadcasting in undirected ad hoc radio networks

We consider distributed broadcasting in radio networks, modeled as undirected graphs, whose nodes have no information on the topology of the network, nor even on their immediate neighborhood. For randomized broadcasting, we give an algorithm working in expected time script O sign(D log(n/D) + log ²n) in n-node radio networks of diameter D, which is optimal, as it matches the lower bounds of Alon et al. [1] and Kushilevitz and Mansour [16]. Our algorithm improves the best previously known randomized broadcasting algorithm of Bar-Yehuda, Goldreich and Itai [3], running in expected time script O sign(D log n + log ²n). (In fact, our result holds also in the setting of n-node directed radio networks of radius D.) For deterministic broadcasting, we show the lower bound Ω (n log n/log (n/D)) on broadcasting time in n-node radio networks of diameter D. This implies previously known lower bounds of Bar-Yehuda, Goldreich and Itai [3] and Bruschi and Del Pinto [5], and is sharper than any of them in many cases. We also give an algorithm working in time script O sign(n log n), thus shrinking - for the first time - the gap between the upper and the lower bound on deterministic broadcasting time to a logarithmic factor.