A Unified Approach to Discrepancy Minimization

TL;DR

This paper introduces a flexible, unified stochastic process-based algorithm for discrepancy minimization, capable of recovering and extending various existing results, including bounds for smoothed instances bridging worst-case and random scenarios.

Contribution

The paper presents a novel, unified stochastic approach to discrepancy minimization that generalizes and improves upon existing methods, including bounds for smoothed instances.

Findings

Recovered various state-of-the-art discrepancy bounds.

Derived a new bound for smoothed instances.

Demonstrated the method's flexibility across different scenarios.

Abstract

We study a unified approach and algorithm for constructive discrepancy minimization based on a stochastic process. By varying the parameters of the process, one can recover various state-of-the-art results. We demonstrate the flexibility of the method by deriving a discrepancy bound for smoothed instances, which interpolates between known bounds for worst-case and random instances.