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The Komlos conjecture in discrepancy theory states that for some constant K and for any m by n matrix A whose columns lie in the unit ball there exists a +/- 1 vector x such that the infinity norm of Ax is bounded above by K.
On some combinatorial questions in finite-dimensional spaces
I. Bárány and VS Grinberg · 1981
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Integer-making theorems
J. Beck and T. Fiala · 1981
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Discrepancy of set-systems and matrices
L. Lovász, J. Spencer, and K. Vesztergombi · 1986
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The Discrepancy Method
B. Chazelle · 1991
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Ten Lectures on the Probabilistic Method
J. Spencer · 1994
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Discrepancy theory
J. Beck and V.T. Sós · 1996
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Balancing vectors and gaussian measures of n-dimensional convex bodies
W. Banaszczyk · 1998
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Integer sequences and semidefinite programming
L. Lovász · 2000
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Matrix Analysis and Applied Linear Algebra
Carl D. Meyer, editor · 2000
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Constructive algorithms for discrepancy minimization
N. Bansal · 2010
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Geometric Discrepancy: An Illustrated Guide
J. Matousek · 2010
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The determinant bound for discrepancy is almost tight
J. Matoušek · 2011
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Constructive discrepancy minimization by walking on the edges
S. Lovett and R. Meka · 2012
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