Discrepancy of set-systems and matrices
European Journal of Combinatorics
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Discrete Mathematics - Proceedings of the Oberwolfach Meeting "Kombinatorik," January 19-25, 1986
Handbook of combinatorics (vol. 2)
Communication complexity
Improved Approximation Guarantees for Packing and Covering Integer Programs
SIAM Journal on Computing
Matrix rounding under the Lp-discrepancy measure and its application to digital halftoning
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal roundings of sequences and matrices
Nordic Journal of Computing
On the discrepancy of combinatorial rectangles
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Combinatorics, Probability and Computing
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We propose an advanced randomized coloring algorithm for the problem of balanced colorings of hypergraphs (discrepancy problem). Instead of independently coloring the vertices with a random color, we try to use structural information about the hypergraph in the design of the random experiment by imposing suitable dependencies. This yields colorings having smaller discrepancy. We also obtain more information about the coloring, or, conversely, we may enforce the random coloring to have special properties. There are some algorithmic advantages as well. We apply our approach to hypergraphs of d-dimensional boxes and to finite geometries. Among others results, we gain a factor 2^d^/^2 decrease in the discrepancy of the boxes, and reduce the number of random bits needed to generate good colorings for the geometries down to O(n) (from n). The latter also speeds up the corresponding derandomization by a factor of n.