Fast approximation algorithms for a nonconvex covering problem
Journal of Algorithms
Some new bounds for Epsilon-nets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
How to net a lot with little: small &egr;-nets for disks and halfspaces
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Planar orientations with low out-degree and compaction of adjacency matrices
Theoretical Computer Science
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Lectures on Discrete Geometry
Hitting sets when the VC-dimension is small
Information Processing Letters
Independent set of intersection graphs of convex objects in 2D
Computational Geometry: Theory and Applications
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the twenty-fourth annual symposium on Computational geometry
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
Covering points by unit disks of fixed location
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
An Approximation Scheme for Terrain Guarding
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
PTAS for weighted set cover on unit squares
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Algorithms for dominating set in disk graphs: breaking the log n Barrier
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Optimal cover of points by disks in a simple polygon
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
On isolating points using disks
ESA'11 Proceedings of the 19th European conference on Algorithms
Optimal Cover of Points by Disks in a Simple Polygon
SIAM Journal on Computing
| Hi-index | 0.00 |
We consider the problem of computing minimum geometric hitting sets in which, given a set of geometric objects and a set of points, the goal is to compute the smallest subset of points that hit all geometric objects. The problem is known to be strongly NP-hard even for simple geometric objects like unit disks in the plane. Therefore, unless P=NP, it is not possible to get Fully Polynomial Time Approximation Algorithms (FPTAS) for such problems. We give the first PTAS for this problem when the geometric objects are half-spaces in Re3 and when they are an r-admissible set regions in the plane (this includes pseudo-disks as they are 2-admissible). Quite surprisingly, our algorithm is a very simple local search algorithm which iterates over local improvements only.