Randomized Leader Election Protocols in Radio Networks with No Collision Detection

  • Authors:
  • Koji Nakano;Stephan Olariu

  • Affiliations:
  • -;-

  • Venue:
  • ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
  • Year:
  • 2000

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Abstract

The main contribution of this work is to propose energy-efficient randomized leader election protocols for single-hop, single-channel radio networks (RN) that do not have collision detection (CD) capabilities. We first presents a leader election protocol for the case the number n of stations is known beforehand. The protocol runs in O(log f) time slots with no station being awake for more than O(log log f + log f/log n) time slots with probability at least 1 - 1/f for any f ≥ 1. We then present three leader election protocols for the case where n is not known beforehand. The first protocol terminates, with probability exceeding 1 - 1/f, in O((log n)2 + (log f)2) time slots, with no station being awake for more than O(log n + log f) time slots. Clearly, this first protocol terminates in O((log n)2) expected time slots. Our second protocol reduces the expected termination time to O(log n) time slots. This second protocol terminates, with probability exceeding 1 - 1/f in O(f3/5 log n) time slots. Finally, by combining these two protocols, we obtain a third leader election protocol that terminates in O(log n) expected time slots. This latter protocol terminates, with with probability exceeding 1 - 1/f, in O(min((log n)2 + (log f)2, f3/5log n)) time slots, with no station being awake for more than O(log n + log f) time slots.