Abstract
This paper considers the matrix chain product problem. This problem can be solved inO(nlogn) sequential time, while the best known parallel NC algorithm runs inO(log2n) time usingn6/log6nprocessors and inO(log3n) time withO(n2) time–processor product. This paper presents a very fast parallel algorithm for approximately solving the matrix chain product problem and for the problem for finding a near-optimal triangulation of a convex polygon. It runs inO(logn) time on a CREW PRAM and inO(loglogn) time on a COMMON CRCW PRAM. If the dimensions of matrices are integers drawn from a domain [k,…,k+s], we can speed up our algorithm to run inO(logloglog(n+s)) time on a COMMON CRCW PRAM. In all cases the total time–processor product is linear. The algorithm produces solutions for the above problems that are at most[formula](≈0.1547) times the optimal solutions.
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