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Finding All Maximal Contiguous Subsequences of a Sequence of Numbers in O(1) Communication Rounds

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3 Author(s)
Alves, C.E.R. ; Univ. Sao Judas Tadeu, Sao Paulo, Brazil ; Caceres, E.N. ; Siang Wun Song

Given a sequence A of real numbers, we wish to find a list of all nonoverlapping 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 has several applications in Computational Biology and can be solved sequentially in linear time. We present a BSP/CGM algorithm that solves this problem using p processors in 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 speedup and is highly scalable. To our knowledge, there are no previous known parallel BSP/CGM algorithms to solve this problem.

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:24 ,  Issue: 4 )