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08/02/2023
Optimal Online Discrepancy Minimization
We prove that there exists an online algorithm that for any sequence of ...
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05/15/2023
Linear-Sized Sparsifiers via Near-Linear Time Discrepancy Theory
Discrepancy theory provides powerful tools for producing higher-quality ...
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03/26/2023
The Subspace Flatness Conjecture and Faster Integer Programming
In a seminal paper, Kannan and Lovász (1988) considered a quantity μ_KL(...
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10/29/2022
The Vector Balancing Constant for Zonotopes
The vector balancing constant vb(K,Q) of two symmetric convex bodies K,Q...
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07/07/2022
Approximate Carathéodory bounds via Discrepancy Theory
The approximate Carathéodory problem in general form is as follows: Give...
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11/04/2021
A New Framework for Matrix Discrepancy: Partial Coloring Bounds via Mirror Descent
Motivated by the Matrix Spencer conjecture, we study the problem of find...
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08/18/2021
A Tighter Relation Between Hereditary Discrepancy and Determinant Lower Bound
In seminal work, Lovász, Spencer, and Vesztergombi [European J. Combin.,...
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07/13/2021
Tight bounds on the Fourier growth of bounded functions on the hypercube
We give tight bounds on the degree ℓ homogenous parts f_ℓ of a bounded f...
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09/12/2020
Balancing Polynomials in the Chebyshev Norm
Given n polynomials p_1, …, p_n of degree at most n with p_i_∞≤ 1 for i ...
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07/10/2020
Vector Balancing in Lebesgue Spaces
A tantalizing conjecture in discrete mathematics is the one of Komlós, s...
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07/03/2019
