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Communication Dans Un Congrès Année : 2012

The weighted words collector

Résumé

Motivated by applications in bioinformatics, we consider the word collector problem, i.e. the expected number of calls to a random weighted generator of words of length $n$ before the full collection is obtained. The originality of this instance of the non-uniform coupon collector lies in the, potentially large, multiplicity of the words/coupons of a given probability/composition. We obtain a general theorem that gives an asymptotic equivalent for the expected waiting time of a general version of the Coupon Collector. This theorem is especially well-suited for classes of coupons featuring high multiplicities. Its application to a given language essentially necessitates some knowledge on the number of words of a given composition/probability. We illustrate the application of our theorem, in a step-by-step fashion, on three exemplary languages, revealing asymptotic regimes in $\Theta(\mu(n)\cdot n)$ and $\Theta(\mu(n)\cdot \log n)$, where $\mu(n)$ is the sum of weights over words of length $n$.
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Dates et versions

hal-00666399 , version 1 (04-02-2012)
hal-00666399 , version 2 (16-04-2012)

Identifiants

Citer

Jérémie Du Boisberranger, Danièle Gardy, Yann Ponty. The weighted words collector. AOFA - 23rd International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms - 2012, Nicolas, Broutin (INRIA, France) and Luc, Devroye (McGill, Canada), Jun 2012, Montreal, Canada. pp.TBA. ⟨hal-00666399v1⟩
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