On enclosing k points by a circle
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This paper presents randomized algorithms for finding a smallest circle enclosing at least k points of P in the plane and an integer k ⩽ n, which improves on previous results by logarithmic factors.About:
This article is published in Information Processing Letters.The article was published on 1995-02-24 and is currently open access. It has received 63 citations till now.read more
Citations
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Book
Geometric Approximation Algorithms
TL;DR: This book is the first to cover geometric approximation algorithms in detail, and topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings.
Journal ArticleDOI
Random Convex Programs
TL;DR: The relation between RCPVs and chance-constrained problems (CCP) is explored, showing that the optimal objective of an RCPV with the generic constraint removal rule provides, with arbitrarily high probability, an upper bound on the optimal objectives of a corresponding CCP.
Journal ArticleDOI
Efficient algorithms for geometric optimization
Pankaj K. Agarwal,Micha Sharir +1 more
TL;DR: A wide range of applications of parametric searching and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other query-type problems.
Book ChapterDOI
Closest-Point Problems in Computational Geometry
TL;DR: Algorithms and data structures for proximity problems on point sets in ℝ D, including the closest pair problem, the exact and approximate post-office problem, and the problem of constructing spanners are discussed in detail.
Journal ArticleDOI
On geometric optimization with few violated constraints
TL;DR: A general algorithm is given and its efficient implementations for specific geometric problems are discussed, for instance for the problem of computing the smallest circle enclosing all butk of the givenn points in the plane, anO(n logn+k3nε) algorithm.
References
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Proceedings ArticleDOI
Applications of random sampling in computational geometry, II
TL;DR: Asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets, are given.
Journal ArticleDOI
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
TL;DR: It is pointed out that analyses of parallelism in computational problems have practical implications even when multi-processor machines are not available, and a unified framework for cases like this is presented.
Journal ArticleDOI
Finding k points with minimum diameter and related problems
TL;DR: In this article, the authors consider the problem of finding k points of a set S that form a small set under some given measure, and present efficient algorithms for several natural measures including the diameter and variance.
Proceedings ArticleDOI
Iterated nearest neighbors and finding minimal polytypes
David Eppstein,Jeff Erickson +1 more
TL;DR: A new method for finding several types of optimalk-point sets, minimizing perimeter, diameter, circumradius, and related measures, by testing sets of theO(k) nearest neighbors to each point, which is better in a number of ways than previous algorithms, which were based on high-order Voronoi diagrams.
Proceedings ArticleDOI
A fast planar partition algorithm. I
TL;DR: Though the algorithm itself is simple, the global evolution of the partition is complex, which makes the analysis of the algorithm theoretically interesting in its own right.