Abstract
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.
Research supported in part by ONR grant N00014-97-1-0505 and NSF grant CCR- 9820885.
Research supported in part by NSF grant CCR-9732746.
Research performed in part while at AT&T Labs-Research, Florham Park, NJ 07932, and supported in part by NSF grant CCR-9732828.
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Anderson, R., Kannan, S., Karloff, H., Ladner, R.E. (2001). Thresholds and Optimal Binary Comparison Search Trees. In: Hariharan, R., Vinay, V., Mukund, M. (eds) FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2001. Lecture Notes in Computer Science, vol 2245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45294-X_8
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DOI: https://doi.org/10.1007/3-540-45294-X_8
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