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
Level schedules for mixed-model, Just-in-Time processes
Management Science
SIAM Journal on Discrete Mathematics
Lattice approximation and linear discrepency of totally unimodular matrices
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Programming pearls: algorithm design techniques
Communications of the ACM
Combinatorics and Algorithms on Low-Discrepancy Roundings of a Real Sequence
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
The maximum deviation just-in-time scheduling problem
Discrete Applied Mathematics
Linear and Hereditary Discrepancy
Combinatorics, Probability and Computing
Information Processing Letters
Discrepancy-based digital halftoning: automatic evaluation and optimization
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Generating randomized roundings with cardinality constraints and derandomizations
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Rounding of sequences and matrices, with applications
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Integer matrices with constraints on leading partial row and column sums
Discrete Applied Mathematics
Unbiased rounding of rational matrices
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Hi-index | 0.00 |
We show several ways to round a real matrix to an integer one such that the rounding errors in all rows and columns as well as the whole matrix are less than one. This is a classical problem with applications in many fields, in particular, statistics We improve earlier solutions of different authors in two ways. For rounding matrices of size m ×n, we reduce the runtime from O( (mn)2 ) to O(mn log(mn)). Second, our roundings also have a rounding error of less than one in all initial intervals of rows and columns. Consequently, arbitrary intervals have an error of at most two. This is particularly useful in the statistics application of controlled rounding The same result can be obtained via (dependent) randomized rounding. This has the additional advantage that the rounding is unbiased, that is, for all entries yij of our rounding, we have E(yij) = xij, where xij is the corresponding entry of the input matrix