Uncommon suffix tries. Issue 1 (3rd May 2013)

• Record Type: Journal Article
• Authors: Cénac, Peggy; Chauvin, Brigitte; Paccaut, Frédéric; Pouyanne, Nicolas
• Is Part Of: Random structures & algorithms. Volume 46:Issue 1(2015)
• Page Start: 117
• Page End: 141
• Publication Date: 2013-05-03
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20500
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>Common assumptions on the source producing the words inserted in a suffix trie with <italic>n</italic> leaves lead to a <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2d2rhc05" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:10429832:media:rsa20500:rsa20500-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ln</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula> height and saturation level. We provide an example of a suffix trie whose height increases faster than a power of <italic>n</italic> and another one whose saturation level is negligible with respect to <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2d2rhc1q" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:10429832:media:rsa20500:rsa20500-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ln</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:math></alternatives></inline-formula>. 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</p> </abstract>