Combinatorial issues in air traffic optimization

The current airway network used by aircraft is composed of a set of segments that intersect on special points defined by radio beacons emitting signals from the ground. This network leads to excess flight length, which for the European network is estimated to be 8%. In the near future, the Global Positioning System, which can determine precisely the location of aircraft, might allow the design of a network without using any ground fixed radio beacons; therefore, we can project a new skyway network with straight airways between airports, allowing an airway to change level one or more times between its origin and destination to avoid potential conflict points. We present some segment set combinatorial issues to achieve such a network. In particular, we propose heuristics or algorithms for the problems of the maximum clique, the coloring, the N-coloring, and other more general problems of coloring of a set of segments. Finally, we discuss some results based on actual data analysis.