This extended abstract describes and analyses a near-optimal probabilistic algorithm, HYPERLOGLOG, dedicated to estimating the number of distinct elements (the cardinality) of very large data… (More)

Boltzmann models from statistical physics combined with methods from analytic combinatorics give rise to efficient algorithms for the random generation of unlabelled objects. The resulting algorithms… (More)

This extended abstract introduces a new algorithm for the random generation of labelled planar graphs. Its principles rely on Boltzmann samplers as recently developed by Duchon, Flajolet, Louchard,… (More)

This article focuses on a combinatorial structure specific to triangulated plane graphs with quadrangular outer face and no separating triangle, which are called irreducible triangulations. The… (More)

A new algorithm is introduced to estimate the number of distinct flows (or connections) in a data stream. The algorithm maintains an accurate estimate of the number of distinct flows over a sliding… (More)

A d-angulation is a planar map with faces of degree d. We present for each integer d ≥ 3 a bijection between the class of d-angulations of girth d and a class of decorated plane trees. Each of the… (More)

We define and investigate so-called transversal structures related to triangulations without separating triangles, which are equivalent to the regular edge labelings discovered by Kant and He. We… (More)

We present a unified general method for the asymptotic study of graphs from the so-called “subcritical” graph classes, which include the classes of cacti graphs, outerplanar graphs, and… (More)