A constant-factor approximation algorithm for red-blue Set cover with unit disks

Abstract

The main contribution of this paper is the first constant factor approximation algorithm for red-blue set cover problem with unit disks. To achieve this, we first give a polynomial time algorithm for line-separable red-blue set cover problem with unit disks. We next obtain a factor 2 approximation algorithm for strip-separable red-blue set cover problem with unit disks. Finally, we obtain a constant factor approximation algorithm for red-blue set cover problem with unit disks by combining our algorithm for the strip-separable problem with the results of Ambühl et al. Our methods involve a novel decomposition of the optimal solution to line-separable problem into blocks with special structure and extensions of the sweep-line technique of Erlebach and van Leeuwen.