A PTAS for the disk cover problem of geometric objects

Pedro J. de Rezende, Flávio K. Miyazawa, Anderson T. Sasaki
2013 Operations Research Letters  
We present PTASes for the disk cover problem: given geometric objects and a finite set of disk centers, minimize the total cost for covering those objects with disks under a polynomial cost function on the disks' radii. We describe the first FPTAS for covering a line segment when the disk centers form a discrete set, and a PTAS for when a set of geometric objects, described by polynomial algebraic inequalities, must be covered. The latter result holds for any dimension.
doi:10.1016/j.orl.2013.06.014 fatcat:fa37frm7yjblla6j6xfbmovj4i