IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v16y2008i4d10.1007_s10878-008-9151-3.html
   My bibliography  Save this article

Computing monotone disjoint paths on polytopes

Author

Listed:
  • David Avis

    (McGill University)

  • Bohdan Kaluzny

    (McGill University)

Abstract

The Holt-Klee Condition states that there exist at least d vertex-disjoint strictly monotone paths from the source to the sink of a polytopal digraph consisting of the set of vertices and arcs of a polytope P directed by a linear objective function in general position. The study of paths on polytopal digraphs stems from a long standing problem, that of designing a polynomial-time pivot method, or proving none exists. To study disjoint paths it would be useful to have a tool to compute them. Without explicitly computing the digraph we develop an algorithm to compute a maximum cardinality set of source to sink paths in a polytope, even in the presence of degeneracy. The algorithm uses a combination of networks flows, the simplex method, and reverse search. An implementation is available.

Suggested Citation

  • David Avis & Bohdan Kaluzny, 2008. "Computing monotone disjoint paths on polytopes," Journal of Combinatorial Optimization, Springer, vol. 16(4), pages 328-343, November.
  • Handle: RePEc:spr:jcomop:v:16:y:2008:i:4:d:10.1007_s10878-008-9151-3
    DOI: 10.1007/s10878-008-9151-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-008-9151-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10878-008-9151-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Michael J. Todd, 1980. "The Monotonic Bounded Hirsch Conjecture is False for Dimension at Least 4," Mathematics of Operations Research, INFORMS, vol. 5(4), pages 599-601, November.
    2. Fukuda, K. & Terlaky, T., 1999. "On the existence of a short admissible pivot sequence for feasibility and linear optimization problems," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 10(4), pages 431-447.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Francisco Santos, 2013. "Recent progress on the combinatorial diameter of polytopes and simplicial complexes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 426-460, October.
    2. Biressaw C. Wolde & Torbjörn Larsson, 2024. "A steepest feasible direction method for linear programming. Derivation and embedding in the simplex method," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(2), pages 163-182.
    3. Yasuko Matsui & Noriyoshi Sukegawa & Ping Zhan, 2023. "Monotone Diameter of Bisubmodular Polyhedra," SN Operations Research Forum, Springer, vol. 4(4), pages 1-16, December.
    4. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:16:y:2008:i:4:d:10.1007_s10878-008-9151-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.