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An efficient algorithm is presented, based on the well-known algorithm for the traveling salesman problem, for scheduling aircraft arrivals into major terminal areas. The algorithm permits, but strictly limits, reassigning an aircraft from its initial position in the landing order. This limitation is needed so that no aircraft or aircraft category is unduly penalized. Results indicate, for the mix of arrivals investigated, a potential increase in capacity in the 3 to 5 percent range. Furthermore, it is shown that the computation time for the algorithm grows only linearly with problem size.