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 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 $O(\min (n^{\omega },n^2+nh\log h+{\chi }^2))$ time, where $\omega <2.373$ denotes the matrix multiplication exponent and $\chi \in \mathrm{\Omega }(n)\cap O(n^2)$ is the number of edges of the graph of oriented distances. We also provide an alternative algorithm for computing the diameter that runs in $O(n^2\log n)$ time.

我们研究了在n个顶点和h个孔的直线多边形域内的直线链接距离下的直径和半径的计算。我们引入了一个定向距离图来编码域对点之间的距离。这有助于我们解决问题，以便我们可以更有效地搜索候选人。我们的算法同时计算直径和半径$Ø（\mathrm{分}（{ñ}^{\omega }，{ñ}^2+ñH\mathrm{日志}H+{\chi }^2））$ 时间，地点 $\omega <2.373$ 表示矩阵乘法指数，并且 $\chi \in \mathrm{\Omega }（ñ）\cap Ø（{ñ}^2）$是方向距离图的边数。我们还提供了另一种算法来计算在$Ø（{ñ}^2\mathrm{日志}ñ）$ 时间。