Computational geometry: an introduction
Computational geometry: an introduction
Computing
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
A guided tour of Chernoff bounds
Information Processing Letters
Fast and reliable parallel hashing
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
Computing the smallest k-enclosing circle and related problems
Computational Geometry: Theory and Applications
On a class of O(n2) problems in computational geometry
Computational Geometry: Theory and Applications
Static and dynamic algorithms for k-point clustering problems
Journal of Algorithms
Translating a convex polygon to contain a maximum number of points
Computational Geometry: Theory and Applications
A reliable randomized algorithm for the closest-pair problem
Journal of Algorithms
Approximation of convex figures by pairs of rectangles
Computational Geometry: Theory and Applications
Computing the arrangement of curve segments: divide-and-conquer algorithms via sampling
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Product Range Spaces, Sensitive Sampling, and Derandomization
SIAM Journal on Computing
Finding planar regions in a terrain: in practice and with a guarantree
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Computing large planar regions in terrains, with an application to fracture surfaces
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Online geometric reconstruction
Proceedings of the twenty-second annual symposium on Computational geometry
Efficient Sensor Placement for Surveillance Problems
DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
Enclosing weighted points with an almost-unit ball
Information Processing Letters
Covering many or few points with unit disks
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Union of random minkowski sums and network vulnerability analysis
Proceedings of the twenty-ninth annual symposium on Computational geometry
The resilience of WDM networks to probabilistic geographical failures
IEEE/ACM Transactions on Networking (TON)
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Let C be a compact set in R2 and let S be a set of n points in R2. We consider the problem of computing a translate of C that contains the maximum number, 驴*, of points of S. It is known that this problem can be solved in a time that is roughly quadratic in n. We show how random-sampling and bucketing techniques can be used to develop a near-linear-time Monte Carlo algorithm that computes a placement of C containing at least (1 - 驴)驴* points of S, for given 驴 0, with high probability. We also present a deterministic algorithm that solves the 驴-approximate version of the optimal-placement problem and runs in O((n1+驴 + n/驴) log m) time, for arbitrary constant 驴 0, if C is a convex m-gon.