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Analysis of a Class of Tries with Adaptive Multi-digit Branching

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Algorithms and Data Structures (WADS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3608))

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Abstract

We study a class of adaptive multi-digit tries, in which the numbers of digits r n processed by nodes with n incoming strings are such that, in memoryless model (with n → ∞):

\(r_n \longrightarrow \frac{log n}{\eta} (pr.)\)

where η is an algorithm-specific constant. Examples of known data structures from this class include LC-tries (Andersson and Nilsson, 1993), “relaxed” LC-tries (Nilsson and Tikkanen, 1998), tries with logarithmic selection of degrees of nodes, etc. We show, that the average depth D n of such tries in asymmetric memoryless model has the following asymptotic behavior (with n → ∞):

\(D_n = \frac{log log n}{-log(1 - h/\eta)}(1 + o(1))\)

where n is the number of strings inserted in the trie, and h is the entropy of the source. We use this formula to compare performance of known adaptive trie structures, and to predict properties of other possible implementations of tries in this class.

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Author information

Authors and Affiliations

  1. RealNetworks, Inc., 2601 Elliott Avenue, Seattle, WA, 98121, USA

    Yuriy A. Reznik

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  1. Yuriy A. Reznik
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Cheriton School of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada

    Alejandro López-Ortiz

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada

    Jörg-Rüdiger Sack

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© 2005 Springer-Verlag Berlin Heidelberg

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Reznik, Y.A. (2005). Analysis of a Class of Tries with Adaptive Multi-digit Branching. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_7

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  • DOI: https://doi.org/10.1007/11534273_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28101-6

  • Online ISBN: 978-3-540-31711-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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