4 papers
Discrepancy Theory: An Algorithmic and Geometric Perspective
Nikhil Bansal, Aleksandar Nikolov
Combinatorial discrepancy theory is a subject with roots in combinatorics, geometry, and number theory, and with numerous applications to mathematics and computer science. At its c…
Online Graph Balancing and the Power of Two Choices
Nikhil Bansal, Milind Prabhu, Sahil Singla +1
In the classic online graph balancing problem, edges arrive sequentially and must be oriented immediately upon arrival, to minimize the maximum in-degree. For adversarial arrivals,…
Decoupling via Affine Spectral-Independence: Beck-Fiala and Komlós Bounds Beyond Banaszczyk
Nikhil Bansal, Haotian Jiang
The Beck-Fiala Conjecture [Discrete Appl. Math, 1981] asserts that any set system of elements with degree has combinatorial discrepancy . A substantial general…
An Improved Bound for the Beck-Fiala Conjecture
Nikhil Bansal, Haotian Jiang
In 1981, Beck and Fiala [Discrete Appl. Math, 1981] conjectured that given a set system with degree at most (i.e., each column of has at most $…