Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Handbook of combinatorics (vol. 2)
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
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
Semi-Balanced Colorings of Graphs: Generalized 2-Colorings Based on a Relaxed Discrepancy Condition
Graphs and Combinatorics
Computational geometric and combinatorial approaches to digital halftoning
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
Computational geometric and combinatorial approaches to digital halftoning
CATS '06 Proceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 51
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Given a connected weighted graph G = (V,E), we consider a hypergraph HG = (V, PG) corresponding to the set of all shortest paths in G. For a given real assignment a on V satisfying 0≤a(v)≤1, a global rounding α with respect to HG is a binary assignment satisfying that |Σv∈Fa(v)-α(v)| F ∈ PG. We conjecture that there are at most |V| + 1 global roundings for HG, and also the set of global roundings is an affine independent set. We give several positive evidences for the conjecture.