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2020 | OriginalPaper | Chapter

Exact Algorithm for One Cardinality-Weighted 2-Partitioning Problem of a Sequence

Authors : Alexander Kel’manov, Sergey Khamidullin, Anna Panasenko

Published in: Learning and Intelligent Optimization

Publisher: Springer International Publishing

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Abstract

We consider a problem of 2-partitioning a finite sequence of points in Euclidean space into two clusters of the given sizes with some additional constraints. The solution criterion is the minimum of the sum (over both clusters) of weighted intracluster sums of squared distances between the elements of each cluster and its center. The weights of the intracluster sums are equal to the cardinalities of the desired clusters. The center of one cluster is given as input, while the center of the other one is unknown and is determined as a geometric center, i.e. as a point of space equal to the mean of the cluster elements. The following constraints hold: the difference between the indices of two subsequent points included in the first cluster is bounded from above and below by given some constants. It is shown that the considered problem is the strongly NP-hard one. An exact algorithm is proposed for the case of integer-valued input of the problem. This algorithm has a pseudopolynomial running time if the space dimension is fixed.

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Title: Exact Algorithm for One Cardinality-Weighted 2-Partitioning Problem of a Sequence
Authors: Alexander Kel’manov
Sergey Khamidullin
Anna Panasenko
Publisher: Springer International Publishing
Book: Learning and Intelligent Optimization
Print ISBN: 978-3-030-38628-3

Electronic ISBN: 978-3-030-38629-0

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-38629-0_11

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