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Probabilistic Counting Algorithms for Data Base Applications
HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm
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.
Singularity Analysis of Generating Functions
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…
Combinatorial aspects of continued fractions
- P. Flajolet
- MathematicsDiscret. Math.
An introduction to the analysis of algorithms
This chapter discusses methods for Solving Recurrences of Trees, Representations of Trees and Binary Trees, and Analyzing Properties of Permutations with CGFs.
Euler Sums and Contour Integral Representations
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...
Boltzmann Samplers for the Random Generation of Combinatorial Structures
- Philippe Duchon, P. Flajolet, G. Louchard, G. Schaeffer
- Mathematics, Computer ScienceCombinatorics, Probability and Computing
- 1 July 2004
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.
Loglog counting of large cardinalities
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…