Some optimal inapproximability results
Journal of the ACM (JACM)
Some simplified NP-complete problems
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Constrained set-up of the tGAP structure for progressive vector data transfer
Computers & Geosciences
Optimal and topologically safe simplification of building footprints
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
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We present a novel method for the automatic generalization of land cover maps. A land cover map is composed of areas that collectively form a tessellation of the plane and each area is assigned to a land cover class such as lake, forest, or settlement. Our method aggregates areas into contiguous regions of equal class and of size greater than a user-defined threshold. To achieve this goal, some areas need to be enlarged at the expense of others. Given function that defines costs for the transformation between pairs of classes, our method guarantees to return a solution of minimal total cost. The method is based on a mixed integer program (MIP). To process maps with more than 50 areas, heuristics are introduced that lead to an alternative MIP formulation. The effects of the heuristics on the obtained solution and the computation time are discussed. The methods were tested using real data from the official German topographic data set (ATKIS) at scales 1:50.000 and 1:250.000.