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Uncommon Suffix Tries

Abstract : Common assumptions on the source producing the words inserted in a suffix trie with $n$ leaves lead to a $\log n$ height and saturation level. We provide an example of a suffix trie whose height increases faster than a power of $n$ and another one whose saturation level is negligible with respect to $\log n$. Both are built from VLMC (Variable Length Markov Chain) probabilistic sources; they are easily extended to families of sources having the same properties. The first example corresponds to a ''logarithmic infinite comb'' and enjoys a non uniform polynomial mixing. The second one corresponds to a ''factorial infinite comb'' for which mixing is uniform and exponential.
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https://hal.archives-ouvertes.fr/hal-00652952
Contributor : Frédéric Paccaut <>
Submitted on : Tuesday, December 20, 2011 - 9:57:53 AM
Last modification on : Monday, April 19, 2021 - 8:56:43 AM
Long-term archiving on: : Wednesday, March 21, 2012 - 2:24:01 AM

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Identifiers

  • HAL Id : hal-00652952, version 2
  • ARXIV : 1112.4131

Citation

Peggy Cénac, Brigitte Chauvin, Frédéric Paccaut, Nicolas Pouyanne. Uncommon Suffix Tries. 2011. ⟨hal-00652952v2⟩

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