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by N+o( Rounds, Alexander Russell, David Zuckerman
n + O(1) rounds, Journal of Computer and System Sciences 63 (2001
http://www.engr.uconn.edu/~acr/Papers/leader.ps
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Abstract:
In the leader election problem, n players wish to elect a random leader. The difficulty is that some coalition of players may conspire to elect one of its own members. We adopt the perfect information model: all communication is by broadcast, and the bad players have unlimited computational power. Within a round, they may also wait to see the inputs of the good players. A protocol is called resilient if a good leader is elected with probability bounded away from 0. We give a simple, constructive leader election protocol that is resilient against coalitions of size bn, for any b! 1=2. Our protocol takes log n +O(1) rounds, each player sending at most logn bits per round. For any constant k, our protocol can be modified to take k rounds and be resilient against coalitions of size en=(log
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