Fast Approximate Counting and Leader Election in Populations
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We study the problems of leader election and population size counting for population protocols: networks of finite-state anonymous agents that interact randomly under a uniform random scheduler. We show a protocol for leader election that terminates in O(_m(n) ·_2 n) parallel time, where m is a parameter, using O({m, n}) states. By adjusting the parameter m between a constant and n, we obtain a single leader election protocol whose time and space can be smoothly traded off between O(^2 n) to O( n) time and O( n) to O(n) states. Finally, we give a protocol which provides an upper bound n̂ of the size n of the population, where n̂ is at most n^a for some a>1. This protocol assumes the existence of a unique leader in the population and stabilizes in Θ(n) parallel time, using constant number of states in every node, except the unique leader which is required to use Θ(^2n) states.
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