3 research outputs found
A faster dual algorithm for the Euclidean minimum covering ball problem
Dearing and Zeck presented a dual algorithm for the problem of the minimum
covering ball in . Each iteration of their algorithm has a
computational complexity of at least . In this paper we
propose a modification to their algorithm that, together with an implementation
that uses updates to the QR factorization of a suitable matrix, achieves a
iteration.Comment: Latex; 12 pages; typo correcte
A dual Simplex-type algorithm for the smallest enclosing ball of balls and related problems
We define the notion of infimum of a set of points with respect to the second
order cone. This problem can be showed to be equivalent to the minimum ball
containing a set of balls problem and to the maximum intersecting ball problem,
as well as others. We present a dual algorithm which can be viewed as an
extension of the simplex method to solve this problem
A branch-and-bound algorithm for the minimum radius -enclosing ball problem
The minimum -enclosing ball problem seeks the ball with smallest radius
that contains at least~ of~ given points in a general -dimensional
Euclidean space. This problem is NP-hard. We present a branch-and-bound
algorithm on the tree of the subsets of~ 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.Comment: 20 pages, 9 figure