Mind the gap: A study of Tube tour

The problem considered in this paper can be expressed as a question: Is it possible to visit all Tube lines in a day? This is a new type of combinatorial optimization problem which generalizes classic problems like TSP, set cover. It has similarities with classic combinatorial optimization problems and ties with operations research applications. We call the graphs corresponding to the city railway systems subway graphs. Examples and properties of such graphs are described in the paper. We show that our problem is NP-hard. Algorithms solving the problem are proposed and their performance is studied both analytically and experimentally on transportation networks of several big cities of the world.