We develop parallel algorithms for both one-dimensional and two-dimensional versions of the maximum sum problem (or max sum for short) on several interconnection networks. These algorithms are all based on a simple scheme that uses preex sums. To this end, we rst show how to compute preex sums of N elements on a hypercube, a star, and a pancake interconnection network of size p (where p N) in o...

We present efficient sequential and parallel algorithms for the maximum sum (MS) problem, which is to maximize the sum of some shape in the data array. We deal with two MS problems; the maximum subarray (MSA) problem and the maximum convex sum (MCS) problem. In the MSA problem, we find a rectangular part within the given data array that maximizes the sum in it. The MCS problem is to find a conv...

The maximum segment sum problem is to compute, given a list of integers, the largest of the sums of the contiguous segments of that list. This problem specification maps directly onto a cubic-time algorithm; however, there is a very elegant linear-time solution too. The problem is a classic exercise in the mathematics of program construction, illustrating important principles such as calculatio...