IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i12p2712-d1171760.html
   My bibliography  Save this article

The Longest ( s , t )-Path Problem on O -Shaped Supergrid Graphs

Author

Listed:
  • Fatemeh Keshavarz-Kohjerdi

    (Department of Mathematics and Computer Science, Shahed University, Tehran 3319118651, Iran)

  • Ruo-Wei Hung

    (Department of Computer Science and Information Engineering, Chaoyang University of Technology, Wufeng, Taichung 413310, Taiwan)

Abstract

The longest ( s , t ) -path problem on supergrid graphs is known to be NP-complete. However, the complexity of this problem on supergrid graphs with or without holes is still unknown.In the past, we presented linear-time algorithms for solving the longest ( s , t ) -path problem on L -shaped and C -shaped supergrid graphs, which form subclasses of supergrid graphs without holes. In this paper, we will determine the complexity of the longest ( s , t ) -path problem on O -shaped supergrid graphs, which form a subclass of supergrid graphs with holes. These graphs are rectangular supergrid graphs with rectangular holes. It is worth noting that O -shaped supergrid graphs contain L -shaped and C -shaped supergrid graphs as subgraphs, but there is no inclusion relationship between them. We will propose a linear-time algorithm to solve the longest ( s , t ) -path problem on O -shaped supergrid graphs. The longest ( s , t ) -paths of O -shaped supergrid graphs have applications in calculating the minimum trace when printing hollow objects using computer embroidery machines and 3D printers.

Suggested Citation

  • Fatemeh Keshavarz-Kohjerdi & Ruo-Wei Hung, 2023. "The Longest ( s , t )-Path Problem on O -Shaped Supergrid Graphs," Mathematics, MDPI, vol. 11(12), pages 1-26, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2712-:d:1171760
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/12/2712/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/12/2712/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:11:y:2023:i:12:p:2712-:d:1171760. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.