On approximating rectangle tiling and packing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for rectangle tiling and packing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Slice and dice: a simple, improved approximate tiling recipe
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On Rectangular Partitionings in Two Dimensions: Algorithms, Complexity, and Applications
ICDT '99 Proceedings of the 7th International Conference on Database Theory
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Discrete & Computational Geometry
Approximation algorithms for array partitioning problems
Journal of Algorithms
Congressional districting using a TSP-based genetic algorithm
GECCO'03 Proceedings of the 2003 international conference on Genetic and evolutionary computation: PartII
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The National Airspace System (NAS) is designed to accommodate a large number of flights over North America. For purposes of workload limitations for air traffic controllers, the airspace is partitioned into approximately 600 sectors; each sector is observed by one or more controllers. In order to satisfy workload limitations for controllers, it is important that sectors be designed carefully according to the traffic patterns of flights, so that no sector becomes overloaded. We formulate and study the airspace sectorization problem from an algorithmic point-of-view, modeling the problem of optimal sectorization as a geometric partition problem with constraints. The novelty of the problem is that it partitions data consisting of trajectories of moving points, rather than static point set partitioning that is commonly studied. First, we formulate and solve the 1D version of the problem, showing how to partition a line into “sectors” (intervals) according to historical trajectory data. Then, we apply the 1D solution framework to design a 2D sectorization heuristic based on binary space partitions. We also devise partitions based on balanced “pie partitions” of a convex polygon. We evaluate our 2D algorithms experimentally, applying our algorithms to actual historical flight track data for the NAS. We compare the workload balance of our methods to that of the existing set of sectors for the NAS and find that our resectorization yields competitive and improved workload balancing. In particular, our methods yield an improvement by a factor between 2 and 3 over the current sectorization in terms of the time-average and the worst-case workloads of the maximum workload sector. An even better improvement is seen in the standard deviations (over all sectors) of both time-average and worst-case workloads.