Constructive Algorithms for Discrepancy Minimization

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.