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 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 . (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 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 , thus shrinking - for the first time - the gap between the upper and the lower bound on deterministic broadcasting time to a logarithmic factor. Received: 1 August 2003, Accepted: 18 March 2005, Published online: 15 June 2005 Dariusz R. Kowalski: This work was done during the stay of Dariusz Kowalski at the Research Chair in Distributed Computing of the Université du Québec en Outaouais, as a postdoctoral fellow. Research supported in part by KBN grant 4T11C04425. Andrzej Pelc: Research of Andrzej Pelc was supported in part by NSERC discovery grant and by the Research Chair in Distributed Computing of the Université du Québec en Outaouais.