Discrepancy, Bansal's Algorithm and the Determinant Bound
Author(s)
Matousek, Jiri
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Abstract
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.
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NSF, NSA, ONR, IMA, Colleges of Sciences, Computing and Engineering
Date
2012-05
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Proceedings