We study the computation of the diameter and radius under the rectilinear
link distance within a rectilinear polygonal domain of n vertices and h
holes. We introduce a \emph{graph of oriented distances} 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 min{O(nω),O(n2+nhlogh+χ2)} time, where ω<2.373 denotes the matrix
multiplication exponent and χ∈Ω(n)∩O(n2) is the number of
edges of the graph of oriented distances. We also provide a faster algorithm
for computing the diameter that runs in O(n2logn) time