Average-Time Complexity of Gossiping in Radio Networks.

Radio networks model wireless synchronous communication with only one wave frequency used for transmissions. In the problem of many-to-all (M2A) communication, some nodes hold input rumors, and the goal is to have all nodes learn all the rumors. We study the average time complexity of distributed many-to-all communication by deterministic protocols in directed networks under two scenarios: of combined messages, in which all input rumors can be sent in one packet, and of separate messages, in which every rumor requires a separate packet to be transmitted. Let n denote the size of a network and k be the number of nodes activated with rumors; the case when k = n is called gossiping. We give a gossiping protocol for combined messages that works in the average time ${\mathcal O}(n/\log n)$, which is shown to be optimal. For the general M2A communication problem, we show that it can be performed in the average time ${\mathcal O}(\min\{k\log(n/k),n/\log n\})$ with combined messages, and that Ω(k/logn + logn) is a lower bound. We give a gossiping protocol for separate messages that works in the average time ${\mathcal O}(n\log n)$, which is shown to be optimal. For the general M2A communication problem, we develop a protocol for separate messages with the average time ${\mathcal O}(k\log(n/k)\log n)$, and show that Ω(k logn) is a lower bound. [ABSTRACT FROM AUTHOR]