Average-Time Complexity of Gossiping in Radio Networks

  • Bogdan S. Chlebus
  • Dariusz R. Kowalski
  • Mariusz A. Rokicki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4056)


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.


Radio Network Relay Node Average Complexity Communication Task Average Time Complexity 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bogdan S. Chlebus
    • 1
  • Dariusz R. Kowalski
    • 2
  • Mariusz A. Rokicki
    • 1
  1. 1.Department of Computer Science and Eng.UCDHSCDenverUSA
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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