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08/13/2022
Intersection Searching amid Tetrahedra in Four Dimensions
We develop data structures for intersection queries in four dimensions t...
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03/19/2022
Intersection Queries for Flat Semi-Algebraic Objects in Three Dimensions and Related Problems
Let 𝒯 be a set of n planar semi-algebraic regions in ℝ^3 of constant com...
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09/15/2021
Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model
We present subquadratic algorithms in the algebraic decision-tree model ...
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02/15/2021
On Ray Shooting for Triangles in 3-Space and Related Problems
We consider several problems that involve lines in three dimensions, and...
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12/08/2020
On rich lenses in planar arrangements of circles and related problems
We show that the maximum number of pairwise non-overlapping k-rich lense...
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03/21/2020
Testing Polynomials for Vanishing on Cartesian Products of Planar Point Sets
We present subquadratic algorithms, in the algebraic decision-tree model...
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04/21/2019
Constructive Polynomial Partitioning for Algebraic Curves in R^3 with Applications
In 2015, Guth proved that for any set of k-dimensional varieties in R^d ...
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12/26/2018
An Efficient Algorithm for Generalized Polynomial Partitioning and Its Applications
Guth showed that given a family S of n g-dimensional semi-algebraic sets...
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02/24/2018
On Pseudo-disk Hypergraphs
Let F be a family of pseudo-disks in the plane, and P be a finite subset...
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12/08/2017