General Balanced Trees

We show that, in order to achieve efficient maintenance of a balanced binary search tree, no shape restriction other than a logarithmic height is required. The obtained class of trees, general balanced trees, may be maintained at a logarithmic amortized cost with no balance information stored in the nodes. Thus, in the case when amortized bounds are sufficient, there is no need for sophisticated balance criteria. The maintenance algorithms use partial rebuilding. This is important for certain applications and has previously been used with weight-balanced trees. We show that the amortized cost incurred by general balanced trees is lower than what has been shown for weight-balanced trees. Q 1999 Academic Press