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A simplicial algorithm for testing the integral properties of polytopes: A revision


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  • Yang, Z.

    (Tilburg University, Center for Economic Research)

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    Given 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.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1994-89.

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    Date of creation: 1994
    Date of revision:
    Handle: RePEc:dgr:kubcen:199489

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    Related research

    Keywords: Linear Programming; operations research;


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    1. Yang, Z., 1994. "A Simplicial Algorithm for Testing the Integral Property of a Polytope," Papers 9475, Tilburg - Center for Economic Research.
    2. 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.
    3. 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.
    4. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January.
    5. Yang, Z., 1994. "A simplicial algorithm for testing the integral property of a polytope," Discussion Paper 1994-75, Tilburg University, Center for Economic Research.
    6. 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.
    7. 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.
    8. 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.
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