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arXiv · 1707.03387

A branch-and-bound algorithm for the minimum radius $k$-enclosing ball problem

Marta Cavaleiro·Farid Alizadeh
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Abstract

The minimum $k$-enclosing ball problem seeks the ball with smallest radius that contains at least~$k$ of~$m$ given points in a general $n$-dimensional Euclidean space. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of~$k$ points to solve this problem. The nodes on the tree are ordered in a suitable way, which, complemented with a last-in-first-out search strategy, allows for only a small fraction of nodes to be explored. Additionally, an efficient dual algorithm to solve the subproblems at each node is employed.

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Marta Cavaleiro, Farid Alizadeh. 2017-07-11. A branch-and-bound algorithm for the minimum radius $k$-enclosing ball problem. https://arxiv.org/abs/1707.03387

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