This text can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study, and is certain to become the definitive reference on the topic.Expand

This extended abstract describes and analyses a near-optimal probabilistic algorithm, HYPERLOGLOG, dedicated to estimating the number of \emphdistinct elements (the cardinality) of very large data ensembles, and makes it possible to estimate cardinalities well beyond $10^9$ with a typical accuracy of 2% while using a memory of only 1.5 kilobytes.Expand

This work presents a class of methods by which one can translate, on a term-by-term basis, an asymptotic expansion of a function around a dominant singularity into a corresponding asymptotic… Expand

This chapter discusses methods for Solving Recurrences of Trees, Representations of Trees and Binary Trees, and Analyzing Properties of Permutations with CGFs.Expand

This paper develops an approach to the evaluation of Euler sums that involve harmonic numbers, either linearly or nonlinearly. We give explicit formulee for several classes of Euler sums in terms o...

A surprisingly simple framework for the random generation of combinatorial configurations based on what the authors call Boltzmann models is proposed, which can be implemented easily, be analysed mathematically with great precision, and, when suitably tuned, tend to be very efficient in practice.Expand

Using an auxiliary memory smaller than the size of this abstract, the LOGLOG algorithm makes it possible to estimate in a single pass and within a few percents the number of different words in the… Expand