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
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
Small-dimensional linear programming and convex hulls made easy
Discrete & Computational Geometry
Using separation algorithms in fixed dimension
Journal of Algorithms
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
Strongly polynomial-time and NC algorithms for detecting cycles in periodic graphs
Journal of the ACM (JACM)
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
Las Vegas algorithms for linear and integer programming when the dimension is small
Journal of the ACM (JACM)
Fixed-dimensional linear programming queries made easy
Proceedings of the twelfth annual symposium on Computational geometry
Fast algorithms for collision and proximity problems involving moving geometric objects
Computational Geometry: Theory and Applications
Computing depth contours of bivariate point clouds
Computational Statistics & Data Analysis - Special issue on classification
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Efficient algorithms for maximum regression depth
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Optimal point placement for mesh smoothing
Journal of Algorithms
New Lower Bounds for Convex Hull Problems in Odd Dimensions
SIAM Journal on Computing
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Linear programming queries revisited
Proceedings of the sixteenth annual symposium on Computational geometry
An optimal algorithm for hyperplane depth in the plane
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
Lower bounds for computing statistical depth
Computational Statistics & Data Analysis
SIAM Journal on Computing
A Combinatorial Bound for Linear Programming and Related Problems
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Low-Dimensional Linear Programming with Violations
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Efficient computation of location depth contours by methods of computational geometry
Statistics and Computing
Algorithms for bivariate medians and a Fermat--Torricelli problem for lines
Computational Geometry: Theory and Applications - Special issue on the thirteenth canadian conference on computational geometry - CCCG'01
Algorithms for center and Tverberg points
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Towards in-place geometric algorithms and data structures
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Multi-pass geometric algorithms
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms
ACM Transactions on Algorithms (TALG)
Computational Geometry: Theory and Applications
On approximate range counting and depth
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Violator spaces: structure and algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Algorithms for bivariate zonoid depth
Computational Geometry: Theory and Applications
An optimal randomized algorithm for d-variate zonoid depth
Computational Geometry: Theory and Applications
Intersecting convex sets by rays
Proceedings of the twenty-fourth annual symposium on Computational geometry
Output-sensitive algorithms for Tukey depth and related problems
Statistics and Computing
Violator spaces: Structure and algorithms
Discrete Applied Mathematics
Optimal location of transportation devices
Computational Geometry: Theory and Applications
Algorithms for center and Tverberg points
ACM Transactions on Algorithms (TALG)
Approximate center points with proofs
Proceedings of the twenty-fifth annual symposium on Computational geometry
The 2-center problem in three dimensions
Proceedings of the twenty-sixth annual symposium on Computational geometry
Approximate centerpoints with proofs
Computational Geometry: Theory and Applications
High dimensional data analysis using multivariate generalized spatial quantiles
Journal of Multivariate Analysis
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
Ray-shooting depth: computing statistical data depth of point sets in the plane
ESA'11 Proceedings of the 19th European conference on Algorithms
Computing a center-transversal line
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Approximating Tverberg points in linear time for any fixed dimension
Proceedings of the twenty-eighth annual symposium on Computational geometry
Absolute approximation of Tukey depth: Theory and experiments
Computational Geometry: Theory and Applications
The 2-center problem in three dimensions
Computational Geometry: Theory and Applications
A proof of the Oja depth conjecture in the plane
Computational Geometry: Theory and Applications
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We present the first optimal algorithm to compute the maximum Tukey depth (also known as location or halfspace depth) for a non-degenerate point set in the plane. The algorithm is randomized and requires O(n log n) expected time for n data points. In a higher fiexed dimension d ≥ 3, the expected time bound is O(nd-1), which is probably optimal as well. The result is obtained using an interesting variant of the author's randomized optimization technique, capable of solving "implicit" linear-programming-type problems; some other applications of this technique are briefly mentioned.