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

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:416783

Karpinski, M ^[1]; Larmore, L L ^[2]; Rytter, W ^[3]

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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

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
DECISION TREE ANALYSIS
OPTIMIZATION
PARALLEL PROCESSING