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Sequential and parallel subquadratic work algorithms for constructing approximately optimal binary search trees

Conference ·
OSTI ID:416783
 [1];  [2];  [3]
  1. Univ. of Bonn (Germany)
  2. Univ. of Nevada, Las Vegas, NV (United States)
  3. Warsaw Univ. (Poland)

A sublinear time subquadratic work parallel algorithm for construction of an optimal binary search tree, in a special case of practical interest, namely where the frequencies of items to be stored are not too small, is given. A sublinear time subquadratic work parallel algorithm for construction of an approximately optimal binary search tree in the general case is also given. Sub-quadratic work and sublinear time are achieved using a fast parallel algorithm for the column minima problem for Monge matrices developed by Atallah and Kosaraju. The algorithms given in this paper take O(n{sup 0.6}) time with n processors in the CREW PRAM model. Our 29orithms work well if every subtree of the optimal binary search tree of depth {Omega}(log n) has o(n) leaves. We prove that there is a sequential algorithm with subquadratic average-case complexity, by demonstrating that the {open_quotes}small subtree{close_quotes} condition holds with very high probability for a randomly permuted weight sequence. This solves the conjecture posed in liand breaks the quadratic time {open_quotes}barrier{close_quotes} of Knuth`s algorithm. This algorithm can also be parallelized to run in average sublinear time with n processors.

OSTI ID:
416783
Report Number(s):
CONF-960121--
Country of Publication:
United States
Language:
English

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