DeepAI

# Online Discrepancy Minimization via Persistent Self-Balancing Walks

We study the online discrepancy minimization problem for vectors in ℝ^d in the oblivious setting where an adversary is allowed fix the vectors x_1, x_2, …, x_n in arbitrary order ahead of time. We give an algorithm that maintains O(√(log(nd/δ))) discrepancy with probability 1-δ, matching the lower bound given in [Bansal et al. 2020] up to an O(√(loglog n)) factor in the high-probability regime. We also provide results for the weighted and multi-color versions of the problem.

• 23 publications
• 12 publications
• 17 publications
• 25 publications
07/21/2020

### Online Discrepancy Minimization for Stochastic Arrivals

In the stochastic online vector balancing problem, vectors v_1,v_2,…,v_T...
11/13/2021

### Prefix Discrepancy, Smoothed Analysis, and Combinatorial Vector Balancing

A well-known result of Banaszczyk in discrepancy theory concerns the pre...
06/24/2020

### Discrepancy Minimization via a Self-Balancing Walk

We study discrepancy minimization for vectors in ℝ^n under various setti...
10/02/2019

### Online Geometric Discrepancy for Stochastic Arrivals with Applications to Envy Minimization

Consider a unit interval [0,1] in which n points arrive one-by-one indep...
11/11/2021

### Online Discrepancy with Recourse for Vectors and Graphs

The vector-balancing problem is a fundamental problem in discrepancy the...
11/10/2022

### Discrepancy Minimization via Regularization

We introduce a new algorithmic framework for discrepancy minimization ba...
03/16/2019

### On-Line Balancing of Random Inputs

We consider an online vector balancing game where vectors v_t, chosen un...