Bounds for optimal α-β binary trees

In this paper we consider a special kind of binary trees where each right edge is associated with a positive number α and each left edge with a positive number β(α ≦ β). Given α, β and the number of nodes n, an optimal tree is one which minimizes the total weighted path length. An algorithm for constructing an optimal tree for given α, β, n is presented, based on which bounds for balances and total weighted path lengths of optimal trees are derived. © 1977 BIT Foundations.