Technical Report CS0182

Title: Modified Binary Search Trees
Authors: Alon Itai and Michael Rodeh
Abstract: A degegerate node in a binary search tree is a node with only one child. It is shown that on the average, an n-node binary search tree has (n+1)/3 degenerate nodes. Suppose the insertion algorithm is modified as follows: Whenever a new node is to be inserted as a grandchild of a degenerate node, the new node, its parent and its grandparent are replaced by the 3-node full binary tree. This heuristic which is very easy to implement has the effect of reducing the average number of degenerate nodes to (n+1)/7 and the average height by a factor of 6/7, to ~1.188 log2(n) which is only 18.8% more than the optimum.
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