A constant-factor approximation for multi-covering with disks
Santanu Bhowmick, Kasturi Varadarajan, Shi-Ke Xue · 2013
We consider variants of the following multi-covering problem with disks. We are given two point sets Y (servers) and X (clients) in the plane, and a coverage function κ :X -> N. Centered at each server is a single disk whose radius we are free to set. The requirement is that each client x ∈ X be covered by at least κ(x) of the server disks. The objective function we wish to minimize is the sum of the areas of the disks. We present a polynomial time algorithm for this problem achieving an O(1) approximation.