Thresholds and Optimal Binary Comparison Search Trees

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.  2002 Elsevier Science (USA). All rights reserved. ✩ A preliminary abbreviated version of this paper appeared in FSTTCS 2001 [1]. * Corresponding author. E-mail addresses: [email protected] (R. Anderson), [email protected] (S. Kannan), [email protected] (H. Karloff), [email protected] (R.E. Ladner). 1 Research supported in part by ONR grant N00014-97-1-0505 and NSF grant CCR-9820885. 2 Research supported in part by NSF grant CCR-9732746. 3 Research performed in part while at AT&T Labs–Research, Florham Park, NJ 07932, and supported in part by NSF grant CCR-9732828. 0196-6774/02/$ – see front matter  2002 Elsevier Science (USA). All rights reserved. PII: S0196-6774(02) 00 20 31 R. Anderson et al. / Journal of Algorithms 44 (2002) 338–358 339