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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 I percent on the average). [ABSTRACT FROM AUTHOR]

This paper investigates the performance of 35 dynamic memory allocation algorithms when used to service simulation programs as represented by 18 test cases. Algorithm performance was measured in terms of processing time, memory usage, and external memory fragmentation. Algorithms maintaining separate free space lists for each size of memory block used tended to perform quite well compared with other algorithms. Simple algorithms operating on memory ordered lists (without any free list) performed surprisingly well. Algorithms employing power-of-two block sizes had favorable processing requirements hut generally unfavorable memory usage. Algorithms employing LIFO, FIFO, or memory ordered free lists generally performed poorly compared with others. [ABSTRACT FROM AUTHOR]