Conflict detection and planar resolution for air traffic control

An algorithm for planar (i.e. no altitude change) conflict resolution in air traffic control (ATC) is presented. By using the point-line duality in 2D of the parallel coordinates methodology, and a field of particles incorporating the motion constraints associated with the aircraft, a "map" in time-and-space of the conflict as well as the conflict-free regions is obtained. Then the algorithm constructs maneuvers, satisfying the constraints, which move the aircraft in conflict to the nearest available conflict-free trajectories. In the process, it is ensured that the maneuvers do not generate new conflicts. The resolution problem, being in general NP-hard, may require very high complexity even in real situations. The need for real-time solutions is handled by cascading (or running in parallel) the algorithm in levels of increasing complexity O(qN^(p+1)logN), where q and N are the number of allowable maneuvers and the number of aircraft respectively, and where the minimum p=1, 2, ..., R needed to resolve a complex conflict scenario is a measure of the scenarios\´ (i.e. input) complexity. As an illustration, a complex conflict scenario is resolved with complexity O(N²logN). The resolution problem is in a sense "dual" to the interception problem. An example is given where the aforementioned time-space map provides specific solutions of the One-Shot problem, which is in general NP-complete. That is "shots", if they exist, are found which intercept all the aircraft