Selecting a subset of diverse points based on the squared euclidean distance

In this paper we consider two closely related problems of selecting a diverse subset of points with respect to squared Euclidean distance. Given a set of points in Euclidean space, the first problem is to find a subset of a specified size M maximizing the sum of squared Euclidean distances between t...

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Veröffentlicht in:Annals of mathematics and artificial intelligence Jg. 90; H. 7-9; S. 965 - 977
Hauptverfasser: Eremeev, Anton V., Kel’manov, Alexander V., Kovalyov, Mikhail Y., Pyatkin, Artem V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.09.2022
Springer
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Artificial Intelligence
Complex Systems
Complexity
Computer Science
Dynamic programming
Euclidean geometry
Euclidean space
Hardness
Integer programming
Mathematics
Optimization
Polynomials
S702: Lion14
Strong NP-hardness
Given size
Maximum variance
Pseudo-polynomial time
62H30
Euclidean space
Integer instance
Fixed space dimension
68W25
Subset of points
Exact algorithm
90C09
ISSN:1012-2443, 1573-7470
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Zusammenfassung:In this paper we consider two closely related problems of selecting a diverse subset of points with respect to squared Euclidean distance. Given a set of points in Euclidean space, the first problem is to find a subset of a specified size M maximizing the sum of squared Euclidean distances between the chosen points. The second problem asks for a minimum cardinality subset of points, given a constraint on the sum of squared Euclidean distances between them. We consider the computational complexity of both problems and propose exact dynamic programming algorithms in the case of integer input data. If the dimension of the Euclidean space is bounded by a constant, these algorithms have a pseudo-polynomial time complexity. We also develop an FPTAS for the special case of the first problem, where the dimension of the Euclidean space is bounded by a constant.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-021-09773-z