Round Robin is optimal for fault-tolerant broadcasting on wireless networks

  • Authors:
  • Andrea E. F. Clementi;Angelo Monti;Riccardo Silvestri

  • Affiliations:
  • Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, I-00133 Rome, Italy;Dipartimento di Informatica, Università "La Sapienza" di Roma, Rome, Italy;Dipartimento di Informatica, Università "La Sapienza" di Roma, Rome, Italy

  • Venue:
  • Journal of Parallel and Distributed Computing
  • Year:
  • 2004

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Abstract

We study the completion time of broadcast operations on static ad hoc wireless networks in presence of unpredictable and dynamical faults.Concerning oblivious fault-tolerant distributed protocols, we provide an Ω(Dn) lower bound where n is the number of nodes of the network and D is the source eccentricity in the fault-free part of the network. Rather surprisingly, this lower bound implies that the simple Round Robin protocol, working in O(Dn) time, is an optimal fault-tolerant oblivious protocol. Then, we demonstrate that networks of o(n/log n) maximum in-degree admit faster oblivious protocols. Indeed, we derive an oblivious protocol having O(D min{n, Δ log n}) completion time on any network of maximum in-degree Δ.Finally, we address the question whether adaptive protocols can be faster than oblivious ones. We show that the answer is negative at least in the general setting: we indeed prove an Ω(Dn) lower bound when D = Θ(√n). This clearly implies that no (adaptive) protocol can achieve, in general, o(Dn) completion time.