Work

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

Year: 2017

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1707.03387

Authors: Cavaleiro, Marta, Alizadeh, Farid

Language: English

Topic: Computational Geometry and Mesh Generation

Subfield: Computer Graphics and Computer-Aided Design

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2734447786

Cites: 14

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Related to: 10