On the average depth of asymmetric LC-tries

  • Authors:
  • Yuriy A. Reznik

  • Affiliations:
  • RealNetworks, Inc., 2601 Elliott Avenue, Seattle, WA 98121, USA

  • Venue:
  • Information Processing Letters
  • Year:
  • 2005

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Abstract

Andersson and Nilsson have already shown that the average depth D"n of random LC-tries is only @Q(log^*n) when the keys are produced by a symmetric memoryless process, and that D"n=O(loglogn) when the process is asymmetric. In this paper we refine the second estimate by showing that asymptotically (with n-~): D"n~1@hloglogn, where n is the number of keys inserted in a trie, @h=-log(1-h/h"-"~), h=-plogp-qlogq is the entropy of a binary memoryless source with probabilities p, q=1-p (pq), and h"-"~=-logmin(p,q).