Red–Blue k-Center Clustering with Distance Constraints

We consider a variant of the k-center clustering problem in IRd, where the centers can be divided into two subsets—one, the red centers of size p, and the other, the blue centers of size q, such that p+q=k, and each red center and each blue center must be a distance of at least some given α≥0 apart....

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Bibliographic Details
Published inMathematics (Basel) Vol. 11; no. 3; p. 748
Main Authors Eskandari, Marzieh, Khare, Bhavika B., Kumar, Nirman, Sadeghi Bigham, Bahram
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2023
Subjects
Algorithms
Approximation
Clustering
computational geometry
Constraints
facility location
Food science
Graphs
Linear programming
Polynomials
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Summary:We consider a variant of the k-center clustering problem in IRd, where the centers can be divided into two subsets—one, the red centers of size p, and the other, the blue centers of size q, such that p+q=k, and each red center and each blue center must be a distance of at least some given α≥0 apart. The aim is to minimize the covering radius. We provide a bi-criteria approximation algorithm for the problem and a polynomial time algorithm for the constrained problem where all centers must lie on a given line ℓ. Additionally, we present a polynomial time algorithm for the case where only the orientation of the line is fixed in the plane (d=2), although the algorithm works even in IRd by constraining the line to lie in a plane and with a fixed orientation.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11030748