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Discrepancy, Bansal's Algorithm and the Determinant Bound

By Jiri Matousek

Abstract

Proceedings of Graph Theory@Georgia Tech, a conference honoring the 50th Birthday of Robin Thomas, May 7-11, 2012 in the Clough Undergraduate Learning Commons.Recently Nikhil Bansal found a polynomial-time algorithm for computing low-discrepancy colorings, based on semidefinite programming. It makes several existential bounds for the discrepancy of certain set systems, such as all arithmetic progressions on {1,2,... ,n}, constructive, which has been a major open problem in discrepancy theory. We use Bansal's result, together with the duality of semidefinite programming and a linear-algebraic lower bound for discrepancy due to Lovasz, Spencer, and Vesztergombi, to answer an old question of Sos, concerning the maximum possible discrepancy of the union of two set systems.NSF, NSA, ONR, IMA, Colleges of Sciences, Computing and Engineerin

Topics: Bansal's algorithm
Publisher: Georgia Institute of Technology
Year: 2012
OAI identifier: oai:smartech.gatech.edu:1853/44212
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