Lecture 3: Constructive Bounds on Discrepancy

In previous lectures we saw a constructive proof of the Lovasz Local Lemma and an application to a variant of the max-min allocations problem. In this lecture we will continue the topic of algorithmic versions of existential theorems with a recent result due to Bansal [Ban10] that makes Spencer's [Spe85] and Srinavasan's [Sri97] bounds on discrepancy of set systems constructive. What makes Bansal's result particularly interesting is that Spencer's and Srinavasan's arguments were previously thought to be non-constructive in a very strong sense.