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- W2952804479 abstract "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 $n$." @default.
- W2952804479 created "2019-06-27" @default.
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- W2952804479 date "2012-02-04" @default.
- W2952804479 modified "2023-09-25" @default.
- W2952804479 title "The weighted words collector" @default.
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