Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Sorting in c log n parallel steps
Combinatorica
Points, spheres, and separators: a unified geometric approach to graph partitioning
Points, spheres, and separators: a unified geometric approach to graph partitioning
The colored Tverberg's problem and complexes of injective functions
Journal of Combinatorial Theory Series A
The m-core properly contains the m-divisible points in space
Pattern Recognition Letters - Special issue on computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Lectures on Discrete Geometry
Efficient computation of location depth contours by methods of computational geometry
Statistics and Computing
An optimal randomized algorithm for maximum Tukey depth
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
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Given a set S of n points in R3, a point x in R3 is called center point of S if every closed halfspace whose bounding hyperplane passes through x contains at least ⌈n/4⌉ points from S. We present a near-quadratic algorithm for computing the center region, that is the set of all center points, of a set of n points in R3. This is nearly tight in the worst case since the center region can have Ω(n2) complexity. We then consider sets S of 3n points in the plane which are the union of three disjoint sets consisting respectively of n red, n blue, and n green points. A point x in R2 is called a colored Tverberg point of S if there is a partition of S into n triples with one point of each color, so that x lies in all triangles spanned by these triples. We present a first polynomial-time algorithm for recognizing whether a given point is a colored Tverberg point of such a 3-colored set S.