IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v462y2024ics009630032300512x.html
   My bibliography  Save this article

Link fault tolerance of BC networks and folded hypercubes on h-extra r-component edge-connectivity

Author

Listed:
  • Yang, Yayu
  • Zhang, Mingzu
  • Meng, Jixiang

Abstract

Parallel and distributed systems play a significant role in high-performance computing, prompting us to investigate qualitative and quantitative metrics to indicate the fault tolerance and vulnerability of systems. Consider the setup where there are large-scale link malfunctions that disconnect the network and result in various components, each with multiple processors. In this paper, we propose and study the h-extra r-component edge-connectivity of a connected graph G, which is denoted by cλrh(G) and has not been addressed before. Let h and r be two positive integers with r≥2. An edge subset F⊆E(G) is said to be an h-extra r-component edge-cut of G, if any, G−F has at least r components and every component of G−F has at least h vertices. The cardinality of the minimum h-extra r-component edge-cut of G is the h-extra r-component edge-connectivity of G. Let h be a positive integer with the decomposition h=∑i=0t2ki, where ki>ki+1, 0≤i≤t−1. In this paper, we derive a lower bound for the exact value of h-extra 3-component edge-connectivity of BC networks Bn and demonstrate that it is tight for one member of Bn, hypercube Qn, in the interval 1≤h≤2⌊n2⌋−1−1, n≥4. This lower bound is also tight for the exact value of 2c-extra 3-component edge-connectivity of Bn with 0≤c≤n−2, n≥4. Specifically, cλ3h(Qn)=2nh−∑i=0tki2ki+1−∑i=0ti2ki+2−h for 1≤h≤2⌊n2⌋−1−1, n≥4 and cλ32c(Bn)=(2n−2c−1)2c for 0≤c≤n−2, n≥4. Exact value of h-extra 3-component edge-connectivity of n-dimensional folded hypercube FQn, cλ3h(FQn) is 2(n+1)h−∑i=0tki2ki+1−∑i=0ti2ki+2−h for 1≤h≤2⌈n2⌉−1−1, n≥4, and that of 2c-extra 3-component edge-connectivity of FQn, cλ32c(FQn), is (2n−2c+1)2c for 0≤c≤n−2, n≥4.

Suggested Citation

  • Yang, Yayu & Zhang, Mingzu & Meng, Jixiang, 2024. "Link fault tolerance of BC networks and folded hypercubes on h-extra r-component edge-connectivity," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    • Handle: RePEc:eee:apmaco:v:462:y:2024:i:c:s009630032300512x
    DOI: 10.1016/j.amc.2023.128343
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032300512X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128343?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. Qiao, Yalin & Yang, Weihua, 2017. "Edge disjoint paths in hypercubes and folded hypercubes with conditional faults," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 96-101.
    2. Olivier Goldschmidt & Dorit S. Hochbaum, 1994. "A Polynomial Algorithm for the k-cut Problem for Fixed k," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 24-37, February.
    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. Ponce, Diego & Puerto, Justo & Temprano, Francisco, 2024. "Mixed-integer linear programming formulations and column generation algorithms for the Minimum Normalized Cuts problem on networks," European Journal of Operational Research, Elsevier, vol. 316(2), pages 519-538.
    2. Yan T. Yang & Barak Fishbain & Dorit S. Hochbaum & Eric B. Norman & Erik Swanberg, 2014. "The Supervised Normalized Cut Method for Detecting, Classifying, and Identifying Special Nuclear Materials," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 45-58, February.
    3. Marie-Christine Costa & Dominique Werra & Christophe Picouleau, 2011. "Minimum d-blockers and d-transversals in graphs," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 857-872, November.
    4. Yuefang Sun & Chenchen Wu & Xiaoyan Zhang & Zhao Zhang, 2022. "Computation and algorithm for the minimum k-edge-connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1741-1752, October.
    5. Mark Velednitsky & Dorit S. Hochbaum, 0. "Isolation branching: a branch and bound algorithm for the k-terminal cut problem," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-21.
    6. Costa, Marie-Christine & Letocart, Lucas & Roupin, Frederic, 2005. "Minimal multicut and maximal integer multiflow: A survey," European Journal of Operational Research, Elsevier, vol. 162(1), pages 55-69, April.
    7. Dmitry Krushinsky & Boris Goldengorin, 2012. "An exact model for cell formation in group technology," Computational Management Science, Springer, vol. 9(3), pages 323-338, August.
    8. Hiroshi Nagamochi & Shigeki Katayama & Toshihide Ibaraki, 2000. "A Faster Algorithm for Computing Minimum 5-Way and 6-Way Cuts in Graphs," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 151-169, June.
    9. Mark Velednitsky & Dorit S. Hochbaum, 2022. "Isolation branching: a branch and bound algorithm for the k-terminal cut problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1659-1679, October.
    10. Mourad Baïou & Francisco Barahona & Ali Ridha Mahjoub, 2000. "Separation of Partition Inequalities," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 243-254, May.
    11. Alena Otto & Erwin Pesch, 2017. "Operation of shunting yards: train-to-yard assignment problem," Journal of Business Economics, Springer, vol. 87(4), pages 465-486, May.
    12. Yuefang Sun & Chenchen Wu & Xiaoyan Zhang & Zhao Zhang, 0. "Computation and algorithm for the minimum k-edge-connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-12.

    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:eee:apmaco:v:462:y:2024:i:c:s009630032300512x. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.