I am interested in Computational Geometry and read some resource in internet to become professional. Suppose given $n$ unit disk in plane. Each center of disk is the site of that disk. We say disks are connected if for each site $p,q$ there is path between $p,q$. Two disk if that have intersect, then they are connected. We must describe an algorithm in $O(nlog n)$ for checking are disk is connected or not? How we can use voronoi diagram? Because i think there is a relation between this problem and voronoi diagram.
Reference for this question is problem 5 of this document :
I try to relate above problem to motion planing according this link to find a path between two point with some obstacle. In addition, i read some paper such as connectivity of disks. But i get stuck to solve this problem. Any hint be appreciated.