Shortest Paths

Abstract

The traffic in a particular city is controlled by seven groups of technicians in seven major junctions of the city. These seven junctions are labeled A, B, C, D, E, F, and G, and their interconnections along the road network in the city are schematically depicted by the network in Figure 1.1. The numbers next to the connections in the network depict the time in minutes required to go from one end of the connection to the other end. The stations communicate with each other using sophisticated communication equipments. GTC holds a contract for the maintenance of this equipment. If there is a malfunction in the equipment at any of the junctions, GTC dispatches maintenance crew from its base station at junction A to the junction at which the equipment malfunctions.

One major consideration for GTC is to minimize downtime, i.e., the time taken by GTC crew to reach the malfunctioning unit after they are informed of the malfunction. Therefore, the crew at location A need to know the quickest route through which they can reach any of the other six junctions if the need arises.