A Unified Approach to Discrepancy Minimization

Authors Nikhil Bansal, Aditi Laddha, Santosh Vempala

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Author Details

Nikhil Bansal
  • University of Michigan, Ann Arbor, MI, USA
Aditi Laddha
  • Georgia Tech, Atlanta, GA, USA
Santosh Vempala
  • Georgia Tech, Atlanta, GA, USA


We are grateful to Yin Tat Lee and Mohit Singh for helpful discussions.

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Nikhil Bansal, Aditi Laddha, and Santosh Vempala. A Unified Approach to Discrepancy Minimization. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Discrepancy theory
  • smoothed analysis


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