Abstract
We develop a simple combinatorial algorithm for computing the smallest enclosing ball of a set of points in high dimensional Euclidean space. The resulting code is in most cases faster (sometimes significantly) than recent dedicated methods that only deliver approximate results, and it beats off-the-shelf solutions, based e.g. on quadratic programming solvers. The algorithm resembles the simplex algorithm for linear programming; it comes with a Bland-type rule to avoid cycling in presence of degeneracies and it typically requires very few iterations. We provide a fast and robust floating-point implementation whose efficiency is based on a new dynamic data structure for maintaining intermediate solutions.
The code can efficiently handle point sets in dimensions up to 2,000, and it solves instances of dimension 10,000 within hours. In low dimensions, the algorithm can keep up with the fastest computational geometry codes that are available.
Partly supported by the IST Programme of the EU and the Swiss Federal Office for Education and Science as a Shared-cost RTD (FET Open) Project under Contract No IST-2000-26473 (ECG – Effective Computational Geometry for Curves and Surfaces).
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Fischer, K., Gärtner, B., Kutz, M. (2003). Fast Smallest-Enclosing-Ball Computation in High Dimensions. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_57
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DOI: https://doi.org/10.1007/978-3-540-39658-1_57
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