TY - GEN

T1 - Calculational developments of new parallel algorithms for size-constrained maximum-sum segment problems

AU - Morihata, Akimasa

PY - 2012/6/6

Y1 - 2012/6/6

N2 - Parallel algorithms for the one-dimensional and the two-dimensional size-constrained maximum-sum segment problems are proposed. The problem, which is a variant of the classic maximum-sum segment problem, is to locate the segment of the maximum total sum among those whose sizes are in a certain range, say, between l and u. It has several applications including pattern recognition, data mining, and DNA analyses, and the size requirement enables us to exclude trivial or useless results. Our parallel algorithms solve it in time O(n / n/p + log p) for one-dimensional arrays of length n and in time O(n 2(u-l) / p + log p) for n × n two-dimensional arrays on EREW PRAM that consists of p processors. It is worth noting that they achieve asymptotically optimal parallel speedups compared with the best known sequential algorithms that take O(n) and O(n 3) times for the one- and the two-dimensional cases, respectively. Our algorithms are correct by their construction: they are systematically derived from their specifications based on the Bird-Meertens formalism.

AB - Parallel algorithms for the one-dimensional and the two-dimensional size-constrained maximum-sum segment problems are proposed. The problem, which is a variant of the classic maximum-sum segment problem, is to locate the segment of the maximum total sum among those whose sizes are in a certain range, say, between l and u. It has several applications including pattern recognition, data mining, and DNA analyses, and the size requirement enables us to exclude trivial or useless results. Our parallel algorithms solve it in time O(n / n/p + log p) for one-dimensional arrays of length n and in time O(n 2(u-l) / p + log p) for n × n two-dimensional arrays on EREW PRAM that consists of p processors. It is worth noting that they achieve asymptotically optimal parallel speedups compared with the best known sequential algorithms that take O(n) and O(n 3) times for the one- and the two-dimensional cases, respectively. Our algorithms are correct by their construction: they are systematically derived from their specifications based on the Bird-Meertens formalism.

UR - http://www.scopus.com/inward/record.url?scp=84861733832&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-29822-6_18

DO - 10.1007/978-3-642-29822-6_18

M3 - Conference contribution

AN - SCOPUS:84861733832

SN - 9783642298219

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 213

EP - 227

BT - Functional and Logic Programming - 11th International Symposium, FLOPS 2012, Proceedings

T2 - 11th International Symposium onFunctional and Logic Programming, FLOPS 2012

Y2 - 23 May 2012 through 25 May 2012

ER -