DMTCS Proceedings, Discrete Random Walks, DRW'03

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DMTCS Conference vol AC (2003), pp. 243-258


Discrete Random Walks, DRW'03

Cyril Banderier and Christian Krattenthaler (eds.)

DMTCS Conference Volume AC (2003), pp. 243-258

author: Pierre Nicodème
-gram analysis and urn models
keywords: Sequence comparison, Bernoulli model, urn models
abstract: Words of fixed size
are commonly referred to as
-grams. We consider the problem of
-gram filtration, a method commonly used to speed up sequence comparison. We are interested in the statistics of the number of
-grams common to two random texts (where multiplicities are not counted) in the non uniform Bernoulli model. In the exact and dependent model, when omitting border effects, a
-gram in a random sequence depends on the
-grams. In an approximate and independent model, we draw randomly a
-gram at each position, independently of the others positions. Using ball and urn models, we analyze the independent model. Numerical simulations show that this model is an excellent first order approximation to the dependent model. We provide an algorithm to compute the moments.
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reference: Pierre Nicodème (2003),
-gram analysis and urn models, in Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, pp. 243-258
bibtex: For a corresponding BibTeX entry, please consider our BibTeX-file.
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