title: A parallel algorithm for iterating partitions of a finite set into subsets of a given cardinality
metadata.name: dc.contributor.author
metadata.value: Kovshov, Alexander M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-05-22T15:21:41Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-05-22T15:21:41Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kovshov A. M. A parallel algorithm for iterating partitions of a finite set into subsets of a given cardinality. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2020, vol. 16, iss. 1, pp. 50–61.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2020.105
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/17787
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article describes an iterative algorithm for searching partitions of a finite set consisting
  of distinguishable elements into subsets of a given cardinality. The cardinalities of some
  subsets may be the same. The entire algorithm consists of two independent algorithms.
  The first algorithm for each element of the original set determines the cardinality of the
  subset that it will fall into when partitioning. To do this, subsets of the same cardinality
  are united into composite subsets. The elements of the original set are distributed among
  composite subsets. An index array is created to describe partitions. This array of indexes
  indicates which composite subset each element falls into. The length of the index array
  is equal to the cardinality of the original set. Each composite subset has its own index
  in the index array. Iterating over partitions of the original set into composite subsets is
  reduced to iterating over all index permutations in the index array. The second algorithm
  distributes elements within each composite subset over subsets of equal cardinalities. For
  each composite subset, an index array is created that describes which subset each element
  of the composite subset falls into. Iterating over all partitions of a composite subset over
  equally powerful subsets is reduced to iterating over-index permutations. Permutations must
  meet the following condition: the index value must not exceed the ordinal number of its
  place in the permutation. This avoids generating the same permutations. Permutations of
  all index arrays are iterated in lexicographic order. This construction of the algorithm allows
  to split the entire search into independent parts and use parallel calculations. An example
  is considered that shows the consistency of the algorithm and the acceleration of obtaining
  the result when using parallel calculations.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 16; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: exhaustive search algorithms
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: parallel computing
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A parallel algorithm for iterating partitions of a finite set into subsets of a given cardinality
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 50-61.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/17787/1/50-61.pdf
resources.format: Adobe PDF
resources.size: 279,18 kB