Computational geometry: an introduction
Computational geometry: an introduction
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Multistep scattered data interpolation using compactly supported radial basis functions
Journal of Computational and Applied Mathematics - Special issue on scattered data
Mathematical Methods for Curves and Surfaces
Hierarchical scattered data filtering for multilevel interpolation schemes
Mathematical Methods for Curves and Surfaces
Introduction to Algorithms
Adaptive thinning for bivariate scattered data
Journal of Computational and Applied Mathematics
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Given a finite point set Z ⊂ Rd, the covering radius of a nonempty subset X ⊂ Z is the minimum distance rX,Z such that every point in Z is at a distance of at most rX,Z from some point in X. This paper concerns the construction of a sequence of subsets of decreasing sizes, such that their covering radii are small. To this end, a method for progressive data reduction, referred to as scattered data filtering, is proposed. The resulting scheme is a composition of greedy thinning, a recursive point removal strategy, and exchange, a postprocessing local optimization procedure. The paper proves adaptive a priori lower bounds on the minimal covering radii, which allows us to control for any current subset the deviation of its covering radius from the optimal value at run time. Important computational aspects of greedy thinning and exchange are discussed. The good performance of the proposed filtering scheme is finally shown by numerical examples.