Round complexity of leader election and gossiping in bidirectional radio networks

We consider the setting of ad hoc radio networks when the underlying network is bidirectional, the number of nodes in the network n is known and nodes can be assigned labels which are polynomially large in n. For this setting we present a protocol for deterministic gossiping which takes rounds improving upon the previous best result by [L. Gasieniec, A. Pagourtizis, I. Potapov, Deterministic gossiping in radio networks with large labels, Algorithmica 47 (2007) 97–117], who give a complex protocol with the round complexity of , resolving an open problem posed by Gasieniec in the survey article [L. Gasieniec, On efficient gossiping in radio networks, in: Proceedings of Sixteenth International Colloquium on Structural Information and Communication Complexity, SIROCCO 2009, Sirince, Turkey, in: LNCS, vol. 5869, 2010, pp. 2–14].The relationship between the asymptotic round complexity of deterministic Leader Election and Gossiping problem has not been known even for bidirectional networks. The gossiping protocol given by Gasieniec et al. invokes the leader election protocol times. Our gossiping protocol achieves this by a single invocation to the leader election protocol. We then use a known fact about the lower bound for leader election for bidirectional radio networks to conclude that the asymptotic round complexity of deterministic Leader Election and Gossiping is the same for bidirectional networks.