Computational geometry: an introduction
Computational geometry: an introduction
On some distance problems in fixed orientations
SIAM Journal on Computing
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Applications of random sampling to on-line algorithms in computational geometry
Discrete & Computational Geometry
Fully dynamic Delaunay triangulation in logarithmic expected time per operation
Computational Geometry: Theory and Applications
Randomized incremental construction of abstract Voronoi diagrams
Computational Geometry: Theory and Applications
Selected papers from the 12th annual symposium on Computational Geometry
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Facility location in a global view
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
| Hi-index | 0.00 |
In this paper we study the following general MaxMin-optimization problem concerning undesirable (obnoxious) facility location: Given a set of n sites S inside a convex region P, construct m garbage deposit sites Vm such that the minimum distance between these sites Vm and the union of S and Vm, Vm ∪ S, is maximized. We present a general method using Voronoi diagrams to approximately solve two such problems when the sites S's are points and weighted convex polygons (correspondingly, Vm's are points and weighted points and the distances are L2 and weighted respectively). In the latter case we generalize the Voronoi diagrams for disjoint weighted convex polygons in the plane. Our algorithms run in polynomial time and approximate the optimal solutions of the above two problems by a factor of 2.