Uncommon suffix tries. Issue 1 (3rd May 2013) - Cénac, Peggy; Chauvin, Brigitte; Paccaut, Frédéric; Pouyanne, Nicolas
Abstract Common assumptions on the source producing the words inserted in a suffix trie with n leaves lead to a <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2d2rhc05" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />lnn</alternatives> 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 <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2d2rhc1q" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />lnn</alternatives>. Both are built from VLMC (Variable Length Markov Chain) probabilistic sources and are easily extended to families of tries 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. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 117–141, 2015