IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v36y2018i1d10.1007_s10878-018-0281-y.html
   My bibliography  Save this article

Optimum turn-restricted paths, nested compatibility, and optimum convex polygons

Author

Listed:
  • Maurice Queyranne

    (University of British Columbia)

  • Laurence A. Wolsey

    (Université catholique de Louvain)

Abstract

We consider two apparently unrelated classes of combinatorial and geometric optimization problems. First, we give compact extended formulations, i.e., polynomial-size linear programming formulations with integer optima, for optimum path problems with turn restrictions satisfying a nested compatibility condition in acyclic digraphs. We then apply these results to optimum convex polygon problems in the plane, by interpreting certain dynamic programming algorithms as sequences of optimum turn-restricted path problems with nested compatibility in acyclic digraphs. As a result, we derive compact extended formulations for these geometric problems as well.

Suggested Citation

  • Maurice Queyranne & Laurence A. Wolsey, 2018. "Optimum turn-restricted paths, nested compatibility, and optimum convex polygons," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 90-107, July.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-018-0281-y
    DOI: 10.1007/s10878-018-0281-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-018-0281-y
    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/s10878-018-0281-y?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. Eliécer Gutiérrez & Andrés Medaglia, 2008. "Labeling algorithm for the shortest path problem with turn prohibitions with application to large-scale road networks," Annals of Operations Research, Springer, vol. 157(1), pages 169-182, January.
    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. Di Puglia Pugliese, Luigi & Guerriero, Francesca, 2013. "Shortest path problem with forbidden paths: The elementary version," European Journal of Operational Research, Elsevier, vol. 227(2), pages 254-267.
    2. Ari, Ibrahim & Aksakalli, Vural & Aydogˇdu, Volkan & Kum, Serdar, 2013. "Optimal ship navigation with safety distance and realistic turn constraints," European Journal of Operational Research, Elsevier, vol. 229(3), pages 707-717.
    3. Thibaut Vidal, 2017. "Node, Edge, Arc Routing and Turn Penalties: Multiple Problems—One Neighborhood Extension," Operations Research, INFORMS, vol. 65(4), pages 992-1010, August.

    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:36:y:2018:i:1:d:10.1007_s10878-018-0281-y. 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.