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Boys-and-girls Birthdays and Hadamard Products.
- Source :
- Fundamenta Informaticae; 2012, Vol. 117 Issue 1-4, p85-101, 17p, 1 Diagram, 1 Graph
- Publication Year :
- 2012
-
Abstract
- Boltzmann models from statistical physics, combined with methods from analytic combinatorics, give rise to efficient and easy-to-write algorithms for the random generation of combinatorial objects. This paper proposes to extend Boltzmann generators to a new field of applications by uniformly sampling a Hadamard product. Under an abstract real-arithmetic computation model, our algorithm achieves approximate-size sampling in expected time ${\cal O}$(n${\sqrt n}$) or ${\cal O}$(nσ) depending on the objects considered, with σ the standard deviation of smallest order for the component object sizes. This makes it possible to generate random objects of large size on a standard computer. The analysis heavily relies on a variant of the so-called birthday paradox, which can be modelled as an occupancy urn problem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01692968
- Volume :
- 117
- Issue :
- 1-4
- Database :
- Complementary Index
- Journal :
- Fundamenta Informaticae
- Publication Type :
- Academic Journal
- Accession number :
- 76400527
- Full Text :
- https://doi.org/10.3233/fi-2012-689