IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v87y2014icp40-47.html
   My bibliography  Save this article

On a leader election algorithm: Truncated geometric case study

Author

Listed:
  • Kalpathy, Ravi
  • Ward, Mark Daniel

Abstract

Recent work of Kalpathy and Mahmoud (in press) gives very general results for a broad class of fair leader election algorithms. They study the duration of contestants, i.e., the number of rounds a randomly selected contestant stays in the competition and another parameter for the associated tree structure. They present a unifying treatment for leader election algorithms, and they show how perpetuities naturally come about. Their theory, however, produces only trivial asymptotic results for the duration of election for some distributions, such as a truncated geometric distribution. In the case of a truncated geometric distribution, the limiting distribution of the duration of contestants is degenerate, and the method of Kalpathy and Mahmoud (in press) does not yield the precise asymptotics. The goal of this short note is to use an alternative method–namely, the q-series methodology–to make a very precise asymptotic analysis of the rate of decay of the mean and the variance of the duration of the election.

Suggested Citation

  • Kalpathy, Ravi & Ward, Mark Daniel, 2014. "On a leader election algorithm: Truncated geometric case study," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 40-47.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:40-47
    DOI: 10.1016/j.spl.2013.12.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715213004197
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2013.12.020?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. Kalpathy, Ravi & Mahmoud, Hosam M. & Rosenkrantz, Walter, 2013. "Survivors in leader election algorithms," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2743-2749.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Usha, K. & Subha, P. A. & Nayak, Chitra R., 2018. "The route to synchrony via drum head mode and mixed oscillatory state in star coupled Hindmarsh–Rose neural network," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 25-31.
    2. Louchard, Guy & Ward, Mark Daniel, 2015. "The truncated geometric election algorithm: Duration of the election," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 40-48.

    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. Cheng Zhang & Hosam Mahmoud, 2016. "Bivariate Issues in Leader Election Algorithms with Marshall-Olkin Limit Distribution," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 401-418, 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:eee:stapro:v:87:y:2014:i:c:p:40-47. 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: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.