Shortest Paths

Abstract

One of the most common applications of graphs in everyday life is the representation of networks for traffic or data communication. The survey map of german motorways in the official guide ‘Autobahn Service’, the railroad or bus lines in some system of public transportation, or the network of routes an airline offers are represented as graphs without anybody being aware of it. Thus, 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 want the route where it is most unlikely that we encounter a speed control installation). We will mainly consider shortest paths in (directed) graphs in this chapter, and we will see that this question is not only of interest in traffic networks.