Distributed multi-broadcast in unknown radio networks

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

  • Affiliations:
  • Univ. of Rome;Univ. of Rome;Univ. of Rome

  • Venue:
  • Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
  • Year:
  • 2001

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Abstract

One of the most frequent tasks in multi-hop synchronous radio networks is the multi-broadcast operation: it consists in performing r independent message broadcasts through a network of n nodes. We investigate the case in which messages have logarithmic bounded size and the nodes have no knowledge of the topology (i.e. unknown networks).Let D and c be the maximum eccentricity and the congestion of the network, respectively. First, we prove an &OHgr;(c+(D+c/log c) log n) lower bound on the number of time-slots required to complete a multi-broadcast operation by any deterministic distributed protocol. Secondly, we prove an &OHgr;(c+(c/log c)log n + D log(n/D)) lower bound for randomized distributed protocols. An important consequence is that “perfect pipeline” is not achievable for both deterministic and randomized protocols.Finally, for any constant &agr; 0, we provide an O((D + c)d2 log(2+&agr;) n) deterministic upper bound for the same task where d is the maximum in-degree of the network. Our (non-constructive) deterministic distributed protocol is thus almost optimal when d = O(polylogn) and it can be converted into an efficiently constructible one having O((D + c)d2 log(3+&agr;) n) completion time.