Shortest Paths

One of the most common applications of graphs in everyday life is representing networks for traffic or for data communication. The schematic map of the German motorway system in the official guide Autobahn Service, the railroad or bus lines in some public transportation system, and the network of routes an airline offers are routinely represented by graphs. Therefore it is obviously of great practical interest to study paths in such graphs. In particular, we often look for paths which are good or even best in some respect: sometimes the shortest or the fastest route is required, sometimes we want the cheapest path or the one which is safest – for example, we might want the route where we are least likely to encounter a speed-control installation. Thus we will study shortest paths in graphs and digraphs in this chapter; as we shall see, this is a topic whose interest extends beyond traffic networks.