Coverage Diameters of Polygons

This paper formalizes and proposes an algorithm to compute coverage diameters of polygons in 2D. Roughly speaking, the coverage diameter of a polygon is the longest possible distance between two points through which the polygon cannot pass in between. The primary use of coverage diameter is to form a cage for transporting an object, not necessarily convex, with multiple disc-shaped robots. The main idea of the computation of coverage diameter is to convert the problem into a graph structure, then perform the search for a solution path in that graph. The proposed algorithm runs in O(n
²
log n) time for the input polygon with n vertices