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2020 | OriginalPaper | Chapter

2-Approximation Polynomial-Time Algorithm for a Cardinality-Weighted 2-Partitioning Problem of a Sequence

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

Published in: Numerical Computations: Theory and Algorithms

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 clusters of the given sizes with some constraints. The solution criterion is the minimum of the sum of weighted intracluster sums of squared distances between the elements of each cluster and its center. The weight of the intracluster sum is equal to the cluster size. The center of one cluster is given as input (is the origin without loss of generality), while the center of the other one is unknown and is determined as a geometric center. 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 some given constants. In this paper, we have shown that the considered problem is the strongly NP-hard one and propose a polynomial-time 2-approximation algorithm for solving the problem.

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previous chapter Multidimensional Global Search Using Numerical Estimations of Minimized Function Derivatives and Adaptive Nested Optimization Scheme

next chapter Exact Linear-Time Algorithm for Parameterized K-Means Problem with Optimized Number of Clusters in the 1D Case

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Title: 2-Approximation Polynomial-Time Algorithm for a Cardinality-Weighted 2-Partitioning Problem of a Sequence
Authors: Alexander Kel’manov
Sergey Khamidullin
Anna Panasenko
Publisher: Springer International Publishing
Book: Numerical Computations: Theory and Algorithms
Print ISBN: 978-3-030-40615-8

Electronic ISBN: 978-3-030-40616-5

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-40616-5_34

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