I. Introduction
Development of advanced air traffic conflict detection and resolution algorithms is imperative to overall health, management, and improvement of the air traffic management (ATM) system, both in Europe and the United States. Eurocontrol and the Federal Aviation Administration (FAA), the respective governing bodies for air traffic control, have recognized the importance of providing some level of automation. In particular, computer aided conflict resolution stands out as a key component of next generation systems, i.e. the Single European Sky ATM Research (SESAR) in Europe [1], and the Next Generation Air Transportation System (NextGen) in the United States [2]. The need for advanced algorithms is especially relevant when one considers issues of safety and capacity within the context of growing air traffic. From 2006 to 2020, the number of instrument flight rules (IFR) aircraft operations handled by FAA enroute traffic centers is predicted to increase from approximately 46 million operations to 70 million operations [3]. As such, the increased demand on the National Airspace System (NAS) will require air traffic controllers to maintain greater situational awareness and to provide safe and robust conflict resolution in real-time. In Europe, similar discussion of enroute capacities leading to enroute delays is reported in [4]. Excluding weather, many of the enroute delays are attributed to staff shortages and lack of capacity planning. It is expected that automated conflict resolution systems will aid in reducing delays while allowing air traffic controllers handle larger workloads.