Sequential and parallel subquadratic work algorithms for constructing approximately optimal binary search trees
- Univ. of Bonn (Germany)
- Univ. of Nevada, Las Vegas, NV (United States)
- 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
Similar Records
Parallel algorithms for separation of two sets of points and recognition of digital convex polygons
Optimal search in trees