Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
On k-hulls and related problems
SIAM Journal on Computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Approximations and optimal geometric divide-and-conquer
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Approximating center points with iterated radon points
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Deterministic sampling and range counting in geometric data streams
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Deterministic sampling and range counting in geometric data streams
ACM Transactions on Algorithms (TALG)
Ray-shooting depth: computing statistical data depth of point sets in the plane
ESA'11 Proceedings of the 19th European conference on Algorithms
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Efficient quantile retrieval on multi-dimensional data
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
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The notion of a centerpoint of a finite set of points in two and higher dimensions is a generalisation of the concept of the median of a (finite) set of points on the real line. In this paper, we present an algorithm for computing a centerpoint of a set of n points in the plane. The algorithm has complexity O(n) which significantly improves the O(n log3 n) complexity of the previously best known algorithm. We use suitable modifications of the ham-sandwich-cut algorithm and the prune-and-search technique to achieve this improvement.