An Algorithm for Komlós Conjecture Matching Banaszczyk's bound

Abstract

We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most t sets. We give an efficient algorithm that finds a coloring with discrepancy O((t log n)^{1/2}), matching the best known non-constructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t^{1/2} log n) bound. The result also extends to the more general Komlós setting and gives an algorithmic O(log^{1/2} n) bound.

References in corpus (3)

• The Komlos Conjecture Holds for Vector Colorings
• Constructive Discrepancy Minimization by Walking on The Edges
• Improved Algorithmic Bounds for Discrepancy of Sparse Set Systems

Cited by in corpus (4)

• Deterministic Discrepancy Minimization via the Multiplicative Weight Update Method
• Online Geometric Discrepancy for Stochastic Arrivals with Applications to Envy Minimization
• The Gram-Schmidt Walk: A Cure for the Banaszczyk Blues
• Tusnády's problem, the transference principle, and non-uniform QMC sampling