On the Complexity of the Problem of Choice of Large Clusters

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2024-08-15 DOI:10.1134/S1990478924020121

A. V. Pyatkin

引用次数: 0

Abstract

The paper considers the following problem. Given a set of Euclidean vectors, find several clusters with a restriction on the maximum scatter of each cluster so that the size of the minimum cluster would be maximum. Here the scatter is the sum of squared distances from the cluster elements to its centroid. The NP-hardness of this problem is proved in the case where the dimension of the space is part of the input.

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论大型集群选择问题的复杂性

摘要本文考虑了以下问题。给定一组欧几里得向量，在限制每个簇的最大散度的情况下找到几个簇，从而使最小簇的大小最大。这里的散度是簇元素到其中心点的距离平方和。在空间维度是输入的一部分的情况下，这个问题的 NP 难度得到了证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.