Theory of linear and integer programming
Theory of linear and integer programming
Embedding of grids into optimal hypercubes
SIAM Journal on Computing
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Level schedules for mixed-model, Just-in-Time processes
Management Science
Embedding grids into hypercubes
Journal of Computer and System Sciences
SIAM Journal on Discrete Mathematics
Matrix Rounding under the Lp-Discrepancy Measure and Its Application to Digital Halftoning
SIAM Journal on Computing
The maximum deviation just-in-time scheduling problem
Discrete Applied Mathematics
Roundings Respecting Hard Constraints
Theory of Computing Systems
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
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Consider the problem of finding an integer matrix that satisfies given constraints on its leading partial row and column sums. For the case in which the specified constraints are merely bounds on each such sum, an integer linear programming formulation is shown to have a totally unimodular constraint matrix. This proves the polynomial-time solvability of this case. In another version of the problem, one seeks a zero-one matrix with prescribed row and column sums, subject to certain near-equality constraints, namely, that all leading partial row (respectively, column) sums up through a given column (respectively, row) are within unity of each other. This case admits a polynomial reduction to the preceding case, and an equivalent reformulation as a maximum-flow problem. The results are developed in a context that relates these two problems to consistent matrix rounding.