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Red–Blue k -Center Clustering with Distance Constraints

Author

Listed:
  • Marzieh Eskandari

    (Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, USA
    Department of Computer Science, Faculty of Mathematical Sciences, Alzahra University, Tehran 19938 93973, Iran)

  • Bhavika B. Khare

    (Department of Computer Science, University of Memphis, Memphis, TN 38152, USA)

  • Nirman Kumar

    (Department of Computer Science, University of Memphis, Memphis, TN 38152, USA)

  • Bahram Sadeghi Bigham

    (Department of Computer Science, Faculty of Mathematical Sciences, Alzahra University, Tehran 19938 93973, Iran
    Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 66731 45137, Iran)

Abstract

We consider a variant of the k -center clustering problem in I R d , 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 I R d by constraining the line to lie in a plane and with a fixed orientation.

Suggested Citation

  • Marzieh Eskandari & Bhavika B. Khare & Nirman Kumar & Bahram Sadeghi Bigham, 2023. "Red–Blue k -Center Clustering with Distance Constraints," Mathematics, MDPI, vol. 11(3), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:748-:d:1054915
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