Author

Nikhil Bansal

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Preprint Aug 2026

An Exposition of the $\widetilde{O}(\log^{1/4} n)$ Bound for the Koml\'os Problem

A conjecture of Koml\'os states that the combinatorial discrepancy of any matrix $A\in\mathbb R^{m\times n}$ whose columns have Euclidean norm at most one is bounded by a universal constant. We prove that the combinatorial discrepancy of every such matrix is at most $O((\log n)^{1/4}(\log\log n)^{7/4})$. This is the fi...

Nikhil Bansal, Hao-Tian Jiang · 0 citations

Preprint Sep 2026

Efficient Algorithms for Subdeterminant Maximization under Partition Matroids

We consider the determinant maximization problem under partition constraints: Given an $n\times n$ PSD matrix A and a partition matroid $M$ on $[n]$, find a base $S$ of $M$ that maximizes $\det(A_{S,S})$. We give an $e^{O(k)}$-approximation algorithm to find such a set $S$, where $k$ is the rank of $M$. This improves u...

Nikhil Bansal, Yu-Ze Xu · 0 citations