On Fourier's Algorithm for Linear Arithmetic (1992)
by
Constraints Jean-Louis Lassez
,
Jean-louis Lassez
,
Michael J. Maher
| Venue: | Journal of Automated Reasoning |
| Citations: | 24 - 4 self |
BibTeX
@ARTICLE{Lassez92onfourier's,
author = {Constraints Jean-Louis Lassez and Jean-louis Lassez and Michael J. Maher},
title = {On Fourier's Algorithm for Linear Arithmetic},
journal = {Journal of Automated Reasoning},
year = {1992},
volume = {9},
pages = {373--379}
}
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Abstract
In the 1820's Fourier provided the first algorithm for solving linear arithmetic constraints. In other words, this algorithm determines whether or not the polyhedral set associated with the constraints is empty. We show here that Fourier's algorithm has an important hidden property: in effect it also computes the affine hull of the polyhedral set. This result is established by making use of a recent theorem on the independence of negative constraints.
Citations
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| 50 | Theory of Linear and Integer - Schrijver - 1998 |
| 34 | A canonical form for generalized linear constraints - Lassez, McAloon - 1992 |
| 20 | Simplification and Elimination of Redundant Linear Arithmetic Constraints - Lassez, Huynh, et al. - 1993 |
| 9 | Parametric queries, linear constraints and variable elimination - Lassez - 1990 |
| 9 | Fourier's method of linear programming and its dual - Williams - 1986 |
| 6 | Minimal Representation of Convex Polyhedral Sets - Telgen - 1982 |
| 4 | Reported in: Analyse des travaux de l'Acadamie Royale des Sciences, pendant l'annee 1824, Partie mathematique, Histoire de l'Academie Royale des Sciences de l'Institut de - Fourier |
| 2 | Random linear programs - ADLER, BERENGUER - 1981 |
| 1 | On Fourier's Analysis of Linear Inequality - Duffin - 1974 |
