Location problems. In a directed G = (N, A) with arc lengths cij, we define the distance between a pair of nodes i and j as the length of the shortest path from node i to node j.
(a) Define the radial distance from node i as the length of the distance from node i to the node farthest from it. We say that a node p is a center of the graph G if node p has as small a radial distance as any node in the network. Suggest a straightforward polynomial-time algorithm for identifying a center of G.
(b) Define the star distance of node i as the total distance from node i to all the nodes in the network. We refer to a node q as a median of G if node q has as small a star distance as any node in the network. Suggest a straightforward polynomial-time algorithm for identifying a median of G.