On a multidimensional search technique and its application to the Euclidean one centre problem
SIAM Journal on Computing
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On weighted rectilinear 2-center and 3-center problems
Information Sciences: an International Journal
Discrete Applied Mathematics - Special issue: graphs in electrical engineering, discrete algorithms and complexity
An efficient algorithm for the Euclidean two-center problem
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Rectilinear and polygonal p-piercing and p-center problems
Proceedings of the twelfth annual symposium on Computational geometry
Rectilinear p-piercing problems
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Faster construction of planar two-centers
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
More planar two-center algorithms
Computational Geometry: Theory and Applications
Discrete rectilinear 2-center problems
Computational Geometry: Theory and Applications
The Capacitated K-Center Problem
SIAM Journal on Discrete Mathematics
The 2-center problem with obstacles
Journal of Algorithms
On Piercing Sets of Axis-Parallel Rectangles and Rings
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Journal of Computer and System Sciences
Optimal geometric partitions, covers and K-centers
MCBE'08 Proceedings of the 9th WSEAS International Conference on Mathematics & Computers In Business and Economics
New Algorithms for k-Center and Extensions
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
| Hi-index | 0.00 |
Rectilinear k-centers of a finite point set P@?R^2 are the centers of at most k congruent axis-parallel squares of minimal size whose union covers P. This paper describes a linear time algorithm based on the prune-and-search paradigm to compute rectilinear 3-centers. The algorithm is elementary in the sense that it does not build on any sophisticated data structures or other algorithms, except for linear time median finding. An implementation is publically available as part of the Computational Geometry Algorithms Library (Cgal).