Title: Constructive Algorithms for Discrepancy Minimization
Speaker: Nikhil Bansal, IBM
Abstract:
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.