Thresholds and optimal binary comparison search trees

Authors:
Richard Anderson;Sampath Kannan;Howard Karloff;Richard E. Ladner
Affiliations:
Department of Computer Science and Engineering, Box 352350, University of Washington, Seattle, WA;AT&T Labs-Research and Department of CIS, University of Pennsylvania, Philadelphia, PA;AT&T Labs-Research, Room C231, Florham Park, NJ 07932 and College of Computing, Georgia Institute of Technology, 801 Atlantic Dr., Atlanta, GA;Department of Computer Science and Engineering, Box 352350, University of Washington, Seattle, WA
Venue:
Journal of Algorithms
Year:
2002

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Abstract

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 comparisons. 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.