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We first formulate the problem of optimally scheduling air traffic low with sector capacity constraints as a mixed integer linear program. We then use semidefinite relaxation techniques to form a convex relaxation of that problem. Finally, we present a randomization algorithm to further improve the quality of the solution. Because of the specific structure of the air traffic flow problem, the relaxation has a single semidefinite constraint of size dn where d is the maximum delay and n the number of flights.
Date of Conference: 5-9 March 2007