Efficient computation of matrix chain

We consider the matrix chain ordering problem to determine the optimal computation order of the matrix chain products. A new algorithm for the matrix chain ordering problem is presented. The time complexity of the presented algorithm is O(n log m), where n is the number of matrices in the chain and m is the number of local minimums in the dimension sequence of the given matrix chain. When m is a fixed constant, the new algorithm requires only O(n) time.