Computing the link center of a simple polygon

The link center of a simple polygon P is the set of points x inside P at which the maximal link-distancefrom x to any other point in P is minimized, where the link distance between two points x, y inside P isdefined as the smallest number of straight edges in a polygonal path inside P connecting x to y. We proveseveral geometric properties of the link center and present an algorithm that calculates this set in time0(n2), where n is the number of sides of P. We also give an 0 (n log n) algorithm for finding apoint x in an approximate link center, namely the maximal link distance from x to any point in P is at most one more than the value attained from the link center.