On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
On arrangements of Jordan arcs with three intersections per pair
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
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
Reporting points in halfspaces
Computational Geometry: Theory and Applications
Fat Triangles Determine Linearly Many Holes
SIAM Journal on Computing
Randomized algorithms
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Computing Many Faces in Arrangements of Lines and Segments
SIAM Journal on Computing
Constructing Levels in Arrangements and Higher Order Voronoi Diagrams
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
SIAM Journal on Computing
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
On the Boundary Complexity of the Union of Fat Triangles
SIAM Journal on Computing
Algorithms for Polytope Covering and Approximation
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
Hitting sets when the VC-dimension is small
Information Processing Letters
Scalable continuous query processing by tracking hotspots
VLDB '06 Proceedings of the 32nd international conference on Very large data bases
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Proceedings of the twenty-fourth annual symposium on Computational geometry
Improved Bounds on the Union Complexity of Fat Objects
Discrete & Computational Geometry
On Approximating the Depth and Related Problems
SIAM Journal on Computing
Efficient Colored Orthogonal Range Counting
SIAM Journal on Computing
Small-size ε-nets for axis-parallel rectangles and boxes
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the set multi-cover problem in geometric settings
Proceedings of the twenty-fifth annual symposium on Computational geometry
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Given a set system (X,R), the hitting set problem is to find a smallest-cardinality subset H ⊆ X, with the property that each range R ∈ R has a non-empty intersection with H. We present near-linear time approximation algorithms for the hitting set problem, under the following geometric settings: (i) R is a set of planar regions with small union complexity. (ii) R is a set of axis-parallel d-rectangles in d-space. In both cases X is either the entire d-dimensional space or a finite set of points in d-space. The approximation factors yielded by the algorithm are small; they are either the same as or within an O(log n) factor of the best factors known to be computable in polynomial time.