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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