Discrepancy of set-systems and matrices
European Journal of Combinatorics
Handbook of combinatorics (vol. 2)
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Lattice approximation and linear discrepency of totally unimodular matrices
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Dispencery in different numbers of colors
Discrete Mathematics
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Recursive Randomized Coloring Beats Fair Dice Random Colorings
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Approximation of Multi-color Discrepancy
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Combinatorics, Probability and Computing
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We investigate the problem to color the vertex set of a hypergraph H = (X, 驴) with a fixed number of colors in a balanced manner, i.e., in such a way that all hyperedges contain roughly the same number of vertices in each color (discrepancy problem). We show the following result:Suppose that we are able to compute for each induced subhypergraph a coloring in c1 colors having discrepancy at most D. Then there are colorings in arbitrary numbers c2 of colors having discrepancy at most 11/10 c12D. A c2-coloring having discrepancy at most 11/10 c12D + 3c1-k|X| can be computed from (c1 - 1)(c2 - 1)k colorings in c1 colors having discrepancy at most D with respect to a suitable subhypergraph of H.A central step in the proof is to show that a fairly general rounding problem (linear discrepancy problem in c2 colors) can be solved by computing low-discrepancy c1-colorings.