Covering the Boundary of a Simple Polygon with Geodesic Unit Disks
  We consider the problem of covering the boundary of a simple polygon on n vertices using the minimum number of geodesic unit disks. We present an O(n \log^2 n+k) time 2-approximation algorithm for finding the centers of the disks, with k denoting the number centers found by the algorithm. 
George Rabanca and Ivo Vigan
cs.CG