On the Height of Height-Balanced Trees

Authors:
Fabrizio Luccio;Linda Pagli
Affiliations:
Istituto di Scienze dell' Informazione, University of Pisa, Pisa, Italy.;Istituto di Scienze dell' Informazione, University of Pisa, Pisa, Italy.
Venue:
IEEE Transactions on Computers
Year:
1976

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Abstract

Height-balanced binary trees with height unbalances up to 驴 are investigated, and the asymptotic value of the height h of such trees is studied for an increasing number of nodes N. It is shown that, in the worst case, the asymptotic value of h is a logarithmic function of N: [h = K log N]n驴驴. Specifically, an upper bound for h can be posed as: h 驴 K1 log (N+2) - K2 for 驴驴 3; and h 驴 K1 log (N+K2) - K3 for 驴 = 4. Less strict bounds are posed for 驴 ≫ 4.