### Interdisciplinary Seminar Series

Title: Constructive Discrepancy Minimization by Walking on the Edges

Speaker: **Raghu Meka**, DIMACS, Rutgers University and IAS

Date: Monday, April 8, 2013 11:00am - 12:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Minimizing the discrepancy of a set system is a fundamental problem in combinatorics. One of the cornerstones in this area is the celebrated six standard deviations result of Spencer (AMS 1985): In any system of n sets in a universe of size n, there always exists a coloring which achieves discrepancy 6sqrt{n}. The original proof of Spencer was existential in nature, and did not give an efficient algorithm to find such a coloring. Recently, a breakthrough work of Bansal (FOCS 2010) gave an efficient algorithm which finds such a coloring. In this work we give a new randomized algorithm to find a coloring as in Spencer's result based on a restricted random walk we call "Edge-Walk". Our algorithm and its analysis use only basic linear algebra and is "truly"constructive in that it does not appeal to the existential arguments, giving a new proof of Spencer's theorem and the partial coloring lemma.

Joint work with Shachar Lovett.

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