An algorithmic version of Banaszczyk's discrepancy theorem

Abstract

In the 90's Banaszczyk developed a very powerful method for discrepancy problems, that goes beyond the partial coloring method. His result was based on deep results from convex geometry and was non-constructive. In this talk, I will present an alternate proof of this result, which is based on elementary techniques and also gives an efficient algorithm. This leads to the first efficient algorithms for several previous results in discrepancy. Based on joint work with Daniel Dadush, Shashwat Garg and Shachar Lovett.