In this paper, we study the leader election problem in the full information model. We show two results in this context. First, we exhibit a constructive O(log N) round protocol that is resilient against linear size coalitions. That is, our protocol is resilient against any coalition of size less then fiN for some constant (but small) value of fi. Second, we provide an easy, non-constructive probabilistic argument that shows the existence of O(log N) round protocol in which fi can be made as large as 1 2 \Gamma ffl for any positive ffl. Our protocols are extremely simple. Preliminary version appeared in STOC y Work done while at Computer Science Division, University of California at Berkeley, and International Computer Science Institute, Berkeley, CA 94720. Email: rafail@bellcore.com. Supported by an NSF Postdoctoral Fellowship and ICSI. z IBM, Almaden. Work done while at Computer Science Division, University of California at Berkeley, CA 94720. Email: sridhar@cs.Berkeley.EDU. ...

Collective coin-flipping is the problem of producing common random bits in a distributed computing environment with adversarial faults. We consider the perfect information model: all communication is by broadcast and corrupt players are computationally unbounded. Protocols in this model may involve many asynchronous rounds; we focus on protocols which permit each player to broadcast a single bit per round. We demonstrate that any n-player coin-flipping protocol resilient against corrupt coalitions of linear size must use \Theta 1=2 \Gamma o(1) log n rounds of communication. Such a bound also applies to the leader election problem. This extends work of Kahn, Kalai, and Linial, who proved a similar result for single-round protocols. The primary component of the above result is a new bound on the influence of random sets of variables on Boolean functions. Finally, in the one-round case, we prove a new bound on the influence of sets of variables of size fin, for fi ? 1=3.

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. Protocols proceed in rounds: though players are synchronized between rounds, within each round the bad players may 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 fin, for any fi ! 1=2. Our protocol takes log

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. Protocols proceed in rounds: though players are synchronized between rounds, within each round the bad players may 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 fin, for any fi ! 1=2. Our protocol takes log

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