Applications of a strategy for designing divide-and-conquer algorithms
Science of Computer Programming
Algebraic identities for program calculation
The Computer Journal - Special issue on Lazy functional programming
FPCA '89 Proceedings of the fourth international conference on Functional programming languages and computer architecture
Science of Computer Programming
Deriving parallel programs from specifications using cost information
Science of Computer Programming
Fast parallel algorithms for the maximum sum problem
Parallel Computing
Formal derivation of efficient parallel programs by construction of list homomorphisms
ACM Transactions on Programming Languages and Systems (TOPLAS)
Mining optimized association rules for numeric attributes
Journal of Computer and System Sciences
Algorithms for the maximum subarray problem based on matrix multiplication
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Make it practical: a generic linear-time algorithm for solving maximum-weightsum problems
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Programming pearls: perspective on performance
Communications of the ACM
Programming pearls: algorithm design techniques
Communications of the ACM
Data Mining with optimized two-dimensional association rules
ACM Transactions on Database Systems (TODS)
Journal of Computer and System Sciences - Computational biology 2002
A Compositional Framework for Mining Longest Ranges
DS '02 Proceedings of the 5th International Conference on Discovery Science
Journal of Functional Programming
An Optimal Algorithm for the Maximum-Density Segment Problem
SIAM Journal on Computing
Journal of Computer and System Sciences
Maximum segment sum is back: deriving algorithms for two segment problems with bounded lengths
PEPM '08 Proceedings of the 2008 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
A compositional framework for developing parallel programs on two-dimensional arrays
International Journal of Parallel Programming
An optimal algorithm for maximum-sum segment and its application in bioinformatics
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Generators-of-generators library with optimization capabilities in fortress
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
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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(n2(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(n3) 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.