Parallel Algorithms for Counting and Randomly Generating Integer Partitions

This paper presents parallel algorithms for determining the number of partitions of a given integerN, where the partitions may be subject to restrictions, such as being composed of distinct parts, of a given number of parts, and/or of parts belonging to a specified set. We present a series of adapti...

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Bibliographic Details
Published inJournal of parallel and distributed computing Vol. 34; no. 1; pp. 29 - 35
Main Authors Sanchis, Laura A., Squire, Matthew B.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 10.04.1996
Elsevier
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Theoretical computing
Multiprocessor
Integer
Partition
Parallel algorithm
Adaptive algorithm
Recurrence relation
Fast algorithm
Time complexity
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Summary:This paper presents parallel algorithms for determining the number of partitions of a given integerN, where the partitions may be subject to restrictions, such as being composed of distinct parts, of a given number of parts, and/or of parts belonging to a specified set. We present a series of adaptive algorithms suitable for varying numbers of processors. The fastest of these algorithms computes the number of partitions ofnwith largest part equal tok, for 1 ≤k≤n≤N, in timeO(log2(N)) usingO(N2/logN) processors. Parallel logarithmic time algorithms that generate partitions uniformly at random, using these quantities, are also presented.
ISSN:0743-7315
1096-0848
DOI:10.1006/jpdc.1996.0043