A BSP/CGM algorithm for finding all maximal contiguous subsequences of a sequence of numbers

Abstract

Given a sequence A of real numbers, we wish to find a list of all non-overlapping contiguous subsequences of A that are maximal. A maximal subsequence M of A has the property that no proper subsequence of M has a greater sum of values. Furthermore, M may not be contained properly within any subsequence of A with this property. This problem can be solved sequentially in linear time. We present a BSP/CGM algorithm that uses p processors and takes O(|A|/p) time and O(|A|/p) space per processor. The algorithm uses a constant number of communication rounds of size at most O(|A|/p). Thus the algorithm achieves linear speed-up and is highly scalable. © Springer-Verlag Berlin Heidelberg 2006.