Rectilinear link diameter and radius in a rectilinear polygonal domain

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of vertices and holes. We introduce a to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in time, where denotes the matrix multiplication exponent and is the number of edges of the graph of oriented distances. We also provide an alternative algorithm for computing the diameter that runs in time.