Red–Blue k-Center Clustering with Distance Constraints

Author:

Eskandari Marzieh12ORCID,Khare Bhavika B.3ORCID,Kumar Nirman3ORCID,Sadeghi Bigham Bahram24ORCID

Affiliation:

1. Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, USA

2. Department of Computer Science, Faculty of Mathematical Sciences, Alzahra University, Tehran 19938 93973, Iran

3. Department of Computer Science, University of Memphis, Memphis, TN 38152, USA

4. Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 66731 45137, Iran

Abstract

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.

Funder

Bahram Sadeghi Bigham

Publisher

MDPI AG

Subject

General Medicine

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3. Linear time algorithms for linear programming in IR3 and related problems;Megiddo;SIAM J. Comput.,1983

4. The slab dividing approach to solve the Euclidean p-center problem;Hwang;Algorithmica,1993

5. Exact and Approximation Algorithms for Clustering;Agarwal;Algorithmica,2002

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