On the average depth of asymmetric LC-tries

  • Authors:
  • Yuriy A. Reznik

  • Affiliations:
  • RealNetworks, Inc., Seattle, WA

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

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Abstract

Andersson and Nilsson have already shown that the average depth Dn of random LC-tries is only Θ(log* n) when the keys are produced by a symmetric memoryless process, and that Dn = O(log logn) when the process is asymmetric. In this paper we refine the second estimate by showing that asymptotically (with n ⇒ ∞): Dn ∼ 1/η log logn, where n is the number of keys inserted in a trie, η = - log(1 - h/h-∞), h = -p log p - q log q is the entropy of a binary, memoryless source with probabilities p, q = 1 - p (p≠q), and h-∞ = - log min(p, q).