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On the average internal path length of m-ary search trees

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Summary

Consider an m-ary tree constructed from a random permutation of size n. When all permutations are equally likely, the average internal path length, which may be considered as a cost measure for searching the tree, is shown to be (n+1)H n/(H m−1)+cn+O(n β),β<1, with

$$c = c(m) = - m/(m - 1) - (H_m - 1)^{ - 1} + A_1^{(m)} $$

, where H kis the k th harmonic number and A (m)1 is a coefficient obtained by solving a linear system of equations. This result tells us that the average cost of searching unbalanced m-ary trees is essentially the same as that of searching other popular variants of m-ary trees like B-trees and B +-trees where sophisticated methods are used for balancing.

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Authors and Affiliations

  1. Department of Statistics, The George Washington University, 20052, Washington, D.C., USA

    Hosam M. Mahmoud

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  1. Hosam M. Mahmoud
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Additional information

This research was supported in part by the Junior Scholar Incentive Program of The George Washington University

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Mahmoud, H.M. On the average internal path length of m-ary search trees. Acta Informatica 23, 111–117 (1986). https://doi.org/10.1007/BF00268078

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  • DOI: https://doi.org/10.1007/BF00268078

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