Thomas Rothvoss | DeepAI

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∙ 08/02/2023

Optimal Online Discrepancy Minimization

We prove that there exists an online algorithm that for any sequence of ...

0 Janardhan Kulkarni, et al. ∙

∙ 07/30/2023

Polytopes with Bounded Integral Slack Matrices Have Sub-Exponential Extension Complexity

We show that any bounded integral function f : A × B ↦{0,1, …, Δ} with r...

0 Sally Dong, et al. ∙

∙ 03/26/2023

The Subspace Flatness Conjecture and Faster Integer Programming

In a seminal paper, Kannan and Lovász (1988) considered a quantity μ_KL(...

0 Victor Reis, et al. ∙

∙ 11/07/2022

From approximate to exact integer programming

Approximate integer programming is the following: For a convex body K ⊆ℝ...

0 Daniel Dadush, et al. ∙

∙ 10/29/2022

The Vector Balancing Constant for Zonotopes

The vector balancing constant vb(K,Q) of two symmetric convex bodies K,Q...

0 Laurel Heck, et al. ∙

∙ 07/07/2022

Approximate Carathéodory bounds via Discrepancy Theory

The approximate Carathéodory problem in general form is as follows: Give...

0 Victor Reis, et al. ∙

∙ 10/05/2021

Approximate CVP in time 2^0.802 n – now in any norm!

We show that a constant factor approximation of the shortest and closest...

0 Thomas Rothvoss, et al. ∙

∙ 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...

0 Siddharth Iyer, et al. ∙

∙ 04/30/2021

On the Hardness of Scheduling With Non-Uniform Communication Delays

In the scheduling with non-uniform communication delay problem, the inpu...

0 Sami Davies, et al. ∙

∙ 07/10/2020

Vector Balancing in Lebesgue Spaces

A tantalizing conjecture in discrete mathematics is the one of Komlós, s...

0 Victor Reis, et al. ∙

∙ 04/21/2020

Scheduling with Communication Delays via LP Hierarchies and Clustering

We consider the classic problem of scheduling jobs with precedence const...

0 Sami Davies, et al. ∙

∙ 07/03/2019

Linear Size Sparsifier and the Geometry of the Operator Norm Ball

The Matrix Spencer Conjecture asks whether given n symmetric matrices in...

0 Victor Reis, et al. ∙

∙ 07/19/2018

A Tale of Santa Claus, Hypergraphs and Matroids

A well-known problem in scheduling and approximation algorithms is the S...

0 Sami Davies, et al. ∙

∙ 06/12/2018

A Fourier-Analytic Approach for the Discrepancy of Random Set Systems

One of the prominent open problems in combinatorics is the discrepancy o...

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