Constructive Algorithms for Discrepancy Minimization
Nikhil Bansal
Dec 01, 2010
The problem of finding the minimum discrepancy coloring is the following: Given a collection of sets S1,...,Sm, color the elements red and blue such that each set is colored as evenly as possible. While several techniques have been developed to show the existence of good colorings, obtaining such colorings algorithmically has been a long standing question.

In this talk, we will describe the first algorithmic results for the problem that essentially match the known existential guarantees. Among other results, we show how to efficiently construct an O(n^{1/2}) discrepancy coloring when m = O(n). This matches the celebrated "six standard deviations suffice" result of Spencer up to constant factors.