Randomized O (log log n)-Round Leader Election Protocols in Packet Radio Networks

  • Authors:
  • Koji Nakano;Stephan Olariu

  • Affiliations:
  • -;-

  • Venue:
  • ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
  • Year:
  • 1998

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Abstract

The main contribution of this work is to propose efficient randomized leader election protocols in Packet Radio Networks (PRN). We show that in a one-channel PRN a leader can be elected among n identical stations in O(log log n) broadcast rounds with probability at least 1 - O(1/log n) or in O(log n) broadcast rounds with probability at least 1- O(1/n). We begin by designing such a protocol for the case where the number n of stations is known beforehand. Next, we show that the leader election can be completed within the same number of broadcast rounds even if n is not known. We show that our protocols are optimal in the sense that no randomized protocol that terminates in o(log n) rounds can elect a leader with probability higher than 1 - O(1/n) and no randomized protocol that terminates in o(log log n) rounds can elect a leader with probability higher than 1 - O(1/log n).