Efficient Matrix Chain Ordering in Polylog Time

The matrix chain ordering problem is to find the cheapest way to multiply a chain of n matrices, where the matrices are pairwise compatible but of varying dimensions. Here we give several new parallel algorithms including O(lg3 n)-time and n/lg n-processor algorithms for solving the matrix chain ordering problem and for solving an optimal triangulation problem of convex polygons on the common CRCW PRAM model. Next, by using efficient algorithms for computing row minima of totally monotone matrices, this complexity is improved to O(lg2 n) time with n processors on the EREW PRAM and to O(lg2 n lg lg n) time with n/lg lg n processors on a common CRCW PRAM. A new algorithm for computing the row minima of totally monotone

• Type: Conference
• Year: 1994
• Where: IPPS
• Authors: Phillip G. Bradford, Gregory J. E. Rawlins, Gregory E. Shannon
• Keywords: Chain Ordering Problem, Common Crcw Pram, Distributed And Parallel Computing, IPPS 1994, Matrix Chain