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A well-known theorem of Spencer shows that any set system with $n$ sets over $n$ elements admits a coloring of discrepancy $O(\sqrt{n})$.
Balancing games
Joel Spencer · 1977
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Roth’s estimate of the discrepancy of integer sequences is nearly sharp
J. Beck · 1981
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“Integer-making” theorems
J. Beck and T. Fiala · 1981
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Six standard deviations suffice
J. Spencer · 1985
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Extremal properties of orthogonal parallelepipeds and their applications to the geometry of banach spaces
E. D. Gluskin · 1989
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On the discrepancy of 3 3 permutations
G. Bohus · 1990
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Matrix analysis
Rajendra Bhatia · 1997
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On some vector balancing problems
A. Giannopoulos · 1997
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Improving the discrepancy bound for sparse matrices: Better approximations for sparse lattice approximation problems
A. Srinivasan · 1997
Cited alongside, same era.
Balancing vectors and Gaussian measures of n n -dimensional convex bodies
W. Banaszczyk · 1998
Cited alongside, same era.
Geometric discrepancy
J. Matoušek · 1999
Cited alongside, same era.
The discrepancy method - randomness and complexity
B. Chazelle · 2001
Cited alongside, same era.
The probabilistic method
N. Alon and J. H. Spencer · 2008
Cited alongside, same era.
Constructive algorithms for discrepancy minimization
N. Bansal · 2010
Cited alongside, same era.
Constructive discrepancy minimization by walking on the edges
S. Lovett and R. Meka · 2012
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Beck’s three permutations conjecture: A counterexample and some consequences
A. Newman, O. Neiman, and A. Nikolov · 2012
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A matrix hyperbolic cosine algorithm and applications
Anastasios Zouzias · 2012
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Deterministic discrepancy minimization
Nikhil Bansal and Joel Spencer · 2013
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Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem
A. Marcus, D. A Spielman, and N. Srivastava · 2013
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The Komlos Conjecture Holds for Vector Colorings
A. Nikolov · 2013
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S. Arora, E. Hazan, and S. Kale · 2012
Cited alongside, same era.
The discrepancy of permutation families
J. H. Spencer, A. Srinivasan, and P. Tetali
Cited in the paper.
Nikhil Bansal, Daniel Dadush, and Shashwat Garg · 2016
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