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

Authors:
Carlos Eduardo Rodrigues Alves;Edson Norberto Cáceres;Siang Wun Song
Affiliations:
Universidade São Judas Tadeu, Brazil;Universidade Federal de Mato Grosso do Sul, Brazil;Universidade de São Paulo, Brazil
Venue:
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Year:
2006

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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.