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

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  • 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
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    References listed on IDEAS

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    1. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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. 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.

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