A simplicial algorithm for testing the integral properties of polytopes: A revision
AbstractGiven an arbitrary polytope P in the n-dimensional Euclidean space R n , the question is to determine whether P contains an integral point or not. We propose a simplicial algorithm to answer this question based on a specifc integer labeling rule and a specific triangulation of R n . Starting from an arbitrary integral point ofR n , the algorithm terminates within a finite number of steps with either an integral point in P or proving there is no integral point inP. One prominent feature of the algorithm is that the structure of the algorithm is very simple and itcanbeeasily implemented on a computer. Moreover, the algorithm is computationally very simple, exible and stable.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1994-89.
Date of creation: 1994
Date of revision:
Contact details of provider:
Web page: http://center.uvt.nl
Linear Programming; operations research;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Yang, Z., 1994. "A Simplicial Algorithm for Testing the Integral Property of a Polytope," Papers 9475, Tilburg - Center for Economic Research.
- Monhein, P., 1976. "Integer Programming and related areas -- a classified bibliography : Ed. by C. Kastning, Lecture Notes in Economics and Mathematical Systems, Operations Research No. 128, Springer-Verlag, Berlin-Heide," Engineering and Process Economics, Elsevier, vol. 1(4), pages 340-341, December.
- Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part II: The Case of Two Activities," Econometrica, Econometric Society, vol. 49(2), pages 395-423, March.
- Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January.
- Yang, Z., 1994. "A simplicial algorithm for testing the integral property of a polytope," Discussion Paper 1994-75, Tilburg University, Center for Economic Research.
- Talman, A.J.J. & Laan, G. van der & Van der Heyden, L., 1987. "Variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using general labelling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153106, Tilburg University.
- Talman, A.J.J. & Laan, G. van der, 1979. "A restart algorithm for computing fixed points without an extra dimension," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153012, Tilburg University.
- Talman, A.J.J. & Laan , G. van der, 1981. "A class of simplicial subdivisions for restart fixed point algorithms," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153024, Tilburg University.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).
If references are entirely missing, you can add them using this form.