Algorithms for clustering data
Algorithms for clustering data
On the complexity of some geometric problems in unbounded dimension
Journal of Symbolic Computation
Inner and outer j-radii of convex bodies in finite-dimensional normed spaces
Discrete & Computational Geometry
A faster algorithm for the two-center decision problem
Information Processing Letters
An efficient algorithm for the Euclidean two-center problem
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
On the complexity of some basic problems in computational convexity: I.: containment problems
Discrete Mathematics - Special issue: trends in discrete mathematics
A near-linear algorithm for the planar 2-center problem
Proceedings of the twelfth annual symposium on Computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Exact and approximation algorithms for clustering
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
More planar two-center algorithms
Computational Geometry: Theory and Applications
Covering a set of points by two axis-parallel boxes
Information Processing Letters
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Clustering Algorithms
The 2-center problem with obstacles
Journal of Algorithms
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Clustering and reconstructing large data sets
Clustering and reconstructing large data sets
A simple linear algorithm for computing rectilinear 3-centers
Computational Geometry: Theory and Applications - Special issue: The 11th Candian conference on computational geometry - CCCG 99
Minimal containment under homothetics: a simple cutting plane approach
Computational Optimization and Applications
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The problem of interest is covering a given point set with homothetic copies of several convex containers C1, ..., Ck, while the objective is to minimize the maximum over the dilatation factors. Such k-containment problems arise in various applications, e.g. in facility location, shape fitting, data classification or clustering. So far most attention has been paid to the special case of the Euclidean k-center problem, where all containers Ciare Euclidean unit balls. New developments based on so-called core-sets enable not only better theoretical bounds in the running time of approximation algorithms but also improvements in practically solvable input sizes. Here, we present some new geometric inequalities and a Mixed-Integer-Convex-Programming formulation. Both are used in a very effective branch-and-bound routine which not only improves on best known running times in the Euclidean case but also handles general and even different containers among the Ci.