Approximate counting with m counters: A probabilistic analysis

Motivated by a recent paper by Cicho\'n and Macyna [1], who introduced $m$ counters (instead of just one) in the approximate counting scheme first analysed by Flajolet [2], we analyse the moments of the sum of the $m$ counters, using techniques that proved to be successful already in several other contexts [11]

Approximate Counting via the Poisson-Laplace-Mellin Method

Approximate counting is an algorithm that provides a count of a huge number of objects within an error tolerance. The first detailed analysis of this algorithm was given by Flajolet. In this paper, we propose a new analysis via the Poisson-Laplace-Mellin approach, a method devised for analyzing shape parameters of digital search trees in a recent paper of Hwang et al. Our approach yields a different and more compact expression for the periodic function from the asymptotic expansion of the variance. We show directly that our expression coincides with the one obtained by Flajolet. Moreover, we apply our method to variations of approximate counting, too

Generalized Approximate Counting Revisited

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