Noncryptographic selection protocols

Selection tasks generalize some well studied problems, such as collective coin flipping and leader election. We present new selection protocols in the full information model, and new negative results. In particular when there are (1+/spl delta/)n/2 good players, we show a protocol that chooses a good leader with probability /spl Omega/(/spl delta//sup 1.65/), and show that every leader election protocol has success probability O(/spl delta//sup 1-/spl epsiv//), for every /spl epsiv/>0. Previously known protocols for this problem have success probability that is exponentially small in 1//spl delta/, and no nontrivial upper bounds on the success probability were known.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[3]  János Komlós,et al.  An 0(n log n) sorting network , 1983, STOC.

[4]  Leslie G. Valiant,et al.  Short Monotone Formulae for the Majority Function , 1984, J. Algorithms.

[5]  Nathan Linial,et al.  The influence of variables on Boolean functions , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[6]  Michael E. Saks.  A Robust Noncryptographic Protocol for Collective Coin Flipping , 1989, SIAM J. Discret. Math..

[7]  Nathan Linial,et al.  Collective Coin Flipping , 1989, Adv. Comput. Res..

[8]  Nathan Linial,et al.  Fault-tolerant computation in the full information model , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[9]  Nathan Linial,et al.  The influence of large coalitions , 1993, Comb..

[10]  Noga Alon,et al.  Coin-Flipping Games Immune Against Linear-Sized Coalitions , 1993, SIAM J. Comput..

[11]  Rafail Ostrovsky,et al.  Simple and efficient leader election in the full information model , 1994, STOC '94.

[12]  N. Linial,et al.  Fast perfect-information leader-election protocols with linear immunity , 1995, Comb..

[13]  D. Zuckerman,et al.  Randomness-optimal oblivious sampling , 1997, Random Struct. Algorithms.

[14]  Alexander Russell,et al.  Perfect information leader election in log*n+O(1) rounds , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[15]  Michael E. Saks,et al.  Lower bounds for leader election and collective coin-flipping in the perfect information model , 1999, STOC '99.

[16]  Ravi B. Boppana,et al.  Perfect-Information Leader Election with Optimal Resilience , 2000, SIAM J. Comput..