Hilbert bases of cones related to simultaneous Diophantine approximations and linear Diophantine equations
Please always quote using this URN: urn:nbn:de:0297-zib-2989
- This paper investigates properties of the minimal integral solutions of a linear diophantine equation. We present best possible inequalities that must be satisfied by these elements which improves on former results. We also show that the elements of the minimal Hilbert basis of the dual cone of all minimal integral solutions of a linear diophantine equation yield best approximations of a rational vector ``from above''. Relations between these cones are applied to the knapsack problem.
Author: | Martin Henk, Robert Weismantel |
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Document Type: | ZIB-Report |
Date of first Publication: | 1997/06/30 |
Series (Serial Number): | ZIB-Report (SC-97-29) |
ZIB-Reportnumber: | SC-97-29 |
Published in: | Appeared in: Combinatorica 22 (3) (2002) 401-408 under the title: Diphantine Approximations and Integer Points of Cones |