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Finding All Maximal Contiguous Subsequences of a Sequence of Numbers in O(1) Communication Rounds
April 2013 (vol. 24 no. 4)
pp. 724-733
C. E. R. Alves, Univ. Sao Judas Tadeu, Sao Paulo, Brazil
E. N. Caceres, Fac. de Comput., Univ. Fed. do Mato Grosso do Sul, Campo Grande, Brazil
Siang Wun Song, Univ. of Sao Paulo, Sao Paulo, Brazil
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.
Index Terms:
Parallel algorithms,Algorithm design and analysis,Program processors,Computational modeling,Materials,Amino acids,Multiprocessor interconnection,communication rounds,All maximal subsequences problem,maximum subsequence problem,parallel algorithm,coarse-grained multicomputer
C. E. R. Alves, E. N. Caceres, Siang Wun Song, "Finding All Maximal Contiguous Subsequences of a Sequence of Numbers in O(1) Communication Rounds," IEEE Transactions on Parallel and Distributed Systems, vol. 24, no. 4, pp. 724-733, April 2013, doi:10.1109/TPDS.2012.149
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