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Lattice approximation and linear discrepency of totally unimodular matrices
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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The maximum deviation just-in-time scheduling problem
Discrete Applied Mathematics
Combinatorics, Probability and Computing
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SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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We show that any real matrix can be rounded to an integer matrix in such a way that the rounding errors of all row sums are less than one, and the rounding errors of all column sums as well as all sums of consecutive row entries are less than two.Such roundings can be computed in linear time. This extends and improves previous results on rounding sequences and matrices in several directions. It has particular applications in just-in-time scheduling, where balanced schedules on machines with negligible switch over costs are sought after. Here we extend existing results to multiple machines and non-constant production rates.