Red blue k-center clustering with distance constraints

07/26/2021

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by   M. Eskandari, et al.

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We consider a variant of the k-center clustering problem in ^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, where p+q=k, and such that each red center and each blue center must be apart a distance of at least some given α≥ 0, with the aim of minimizing 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.