Thresholds and Optimal Binary Comparison Search Trees
We present an O(n 4)-time algorithm for the following problem: Given a set of items with known access frequencies, find the optimal binary search tree under the realistic assumption that each comparison can only result in a two-way decision: either an equality comparison or a less-than comparison. This improves the best known result of O(n 5) time, which is based on split tree algorithms. Our algorithm relies on establishing thresholds on the frequency of an item that can occur as an equality comparison at the root of an optimal tree.
KeywordsSide Branch Main Branch Maximum Probability Optimal Cost Binary Search Tree
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