IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v55y2001i3p239-246.html
   My bibliography  Save this article

On the distribution of the domination number for random class cover catch digraphs

Author

Listed:
  • Priebe, Carey E.
  • DeVinney, Jason G.
  • Marchette, David J.

Abstract

In this article we initiate the study of class cover catch digraphs, a special case of intersection digraphs motivated by applications in machine learning and statistical pattern recognition. Our main result is the exact distribution of the domination number for a data-driven model of random interval catch digraphs.

Suggested Citation

  • Priebe, Carey E. & DeVinney, Jason G. & Marchette, David J., 2001. "On the distribution of the domination number for random class cover catch digraphs," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 239-246, December.
    • Handle: RePEc:eee:stapro:v:55:y:2001:i:3:p:239-246
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(01)00129-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
    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. Ceyhan, Elvan & Priebe, Carey E., 2005. "The use of domination number of a random proximity catch digraph for testing spatial patterns of segregation and association," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 37-50, June.
    2. Wierman, John C. & Xiang, Pengfei, 2008. "A general SLLN for the one-dimensional class cover problem," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1110-1118, July.
    3. Xiang, Pengfei & Wierman, John C., 2009. "A CLT for a one-dimensional class cover problem," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 223-233, January.
    4. Elvan Ceyhan, 2014. "Comparison of relative density of two random geometric digraph families in testing spatial clustering," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 100-134, March.
    5. Elvan Ceyhan, 2012. "The distribution of the relative arc density of a family of interval catch digraph based on uniform data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 761-793, August.
    6. Elvan Ceyhan, 2012. "An Investigation of New Graph Invariants Related to the Domination Number of Random Proximity Catch Digraphs," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 299-334, June.
    7. Ceyhan, Elvan & Priebe, Carey E. & Wierman, John C., 2006. "Relative density of the random r-factor proximity catch digraph for testing spatial patterns of segregation and association," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1925-1964, April.
    8. Priebe, Carey E. & Solka, Jeffrey L. & Marchette, David J. & Clark, B. Ted, 2003. "Class cover catch digraphs for latent class discovery in gene expression monitoring by DNA microarrays," Computational Statistics & Data Analysis, Elsevier, vol. 43(4), pages 621-632, August.

    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. Larry W. Jacobs & Michael J. Brusco, 1995. "Note: A local‐search heuristic for large set‐covering problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(7), pages 1129-1140, October.
    2. Raka Jovanovic & Antonio P. Sanfilippo & Stefan Voß, 2022. "Fixed set search applied to the multi-objective minimum weighted vertex cover problem," Journal of Heuristics, Springer, vol. 28(4), pages 481-508, August.
    3. Imran Khan & Naveed Riaz, 2015. "A new and fast approximation algorithm for vertex cover using a maximum independent set (VCUMI)," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 25(4), pages 5-18.
    4. Pál Pusztai, 2008. "An application of the greedy heuristic of set cover to traffic checks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 407-414, December.
    5. Jia Shu, 2010. "An Efficient Greedy Heuristic for Warehouse-Retailer Network Design Optimization," Transportation Science, INFORMS, vol. 44(2), pages 183-192, May.
    6. Davidov, Sreten & Pantoš, Miloš, 2017. "Planning of electric vehicle infrastructure based on charging reliability and quality of service," Energy, Elsevier, vol. 118(C), pages 1156-1167.
    7. Lakmali Weerasena & Aniekan Ebiefung & Anthony Skjellum, 2022. "Design of a heuristic algorithm for the generalized multi-objective set covering problem," Computational Optimization and Applications, Springer, vol. 82(3), pages 717-751, July.
    8. Filipe Rodrigues & Agostinho Agra & Lars Magnus Hvattum & Cristina Requejo, 2021. "Weighted proximity search," Journal of Heuristics, Springer, vol. 27(3), pages 459-496, June.
    9. Lan, Guanghui & DePuy, Gail W. & Whitehouse, Gary E., 2007. "An effective and simple heuristic for the set covering problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1387-1403, February.
    10. Giovanni Felici & Sokol Ndreca & Aldo Procacci & Benedetto Scoppola, 2016. "A-priori upper bounds for the set covering problem," Annals of Operations Research, Springer, vol. 238(1), pages 229-241, March.
    11. Parra Inza, Ernesto & Vakhania, Nodari & Sigarreta Almira, José María & Hernández Mira, Frank Angel, 2024. "Exact and heuristic algorithms for the domination problem," European Journal of Operational Research, Elsevier, vol. 313(3), pages 926-936.
    12. Song, Zhe & Kusiak, Andrew, 2010. "Mining Pareto-optimal modules for delayed product differentiation," European Journal of Operational Research, Elsevier, vol. 201(1), pages 123-128, February.
    13. Seona Lee & Sang-Ho Lee & HyungJune Lee, 2020. "Timely directional data delivery to multiple destinations through relay population control in vehicular ad hoc network," International Journal of Distributed Sensor Networks, , vol. 16(5), pages 15501477209, May.
    14. Yingli Ran & Yishuo Shi & Zhao Zhang, 2017. "Local ratio method on partial set multi-cover," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 302-313, July.
    15. Zhuang, Yanling & Zhou, Yun & Yuan, Yufei & Hu, Xiangpei & Hassini, Elkafi, 2022. "Order picking optimization with rack-moving mobile robots and multiple workstations," European Journal of Operational Research, Elsevier, vol. 300(2), pages 527-544.
    16. Menghong Li & Yingli Ran & Zhao Zhang, 2022. "A primal-dual algorithm for the minimum power partial cover problem," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1913-1923, October.
    17. Zhengyu Ma & Hong Seo Ryoo, 2021. "Spherical Classification of Data, a New Rule-Based Learning Method," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 44-71, April.
    18. Lim, Seow & Kuby, Michael, 2010. "Heuristic algorithms for siting alternative-fuel stations using the Flow-Refueling Location Model," European Journal of Operational Research, Elsevier, vol. 204(1), pages 51-61, July.
    19. Sebastian Abshoff & Peter Kling & Christine Markarian & Friedhelm Meyer auf der Heide & Peter Pietrzyk, 2016. "Towards the price of leasing online," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1197-1216, November.
    20. Gopalan, Ram, 2014. "The Aircraft Maintenance Base Location Problem," European Journal of Operational Research, Elsevier, vol. 236(2), pages 634-642.

    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:55:y:2001:i:3:p:239-246. 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.