An O(n) Algorithm for Determining a Near-Optimal
Computation Order of Matrix Chain Products

This paper discusses the computation of matrix
chain products of the form M1 x M2 x ... x Mn 
where Mi's are matrices.  The order in which the matrices
are computed affects the number of operations. 
 A sufficient condition about the association of the
matrices in the optimal order is presented.  An 
O(n) algorithm to find an order of computation which
takes less than 25 percent longer than the optimal 
time Topt is also presented.  In most cases, the algorithm
yields the optimal order or an order which 
takes only a few percent longer than Topt (less than 1 percent on the average).

CACM July, 1978

Chin, F.

Approximate algorithm, heuristic algorithm,
matrix multiplication, matrix chain product

5.14

CA780703 DH February 8, 1979  2:46 PM

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