Journal of Algorithms
Optimal search trees using two-way key comparisons
Acta Informatica
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Efficient multiple and predicated dispatching
Proceedings of the 14th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
Median split trees: a fast lookup technique for frequently occuring keys
Communications of the ACM
Information Theory and Reliable Communication
Information Theory and Reliable Communication
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We present an O(n4)-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(n5) 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.