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All issues Volume 25 (2021) ESAIM: PS, 25 (2021) 376-407 References
Open Access
Issue
ESAIM: PS
Volume 25, 2021
Page(s) 376 - 407
DOI https://doi.org/10.1051/ps/2021013
Published online 27 July 2021
  1. M.A. Akcoglu and U. Krengel, Ergodic theorems for superadditive processes. Journal für die Reine und Angewandte Mathematik 323 (1981) 53–67. [Google Scholar]
  2. A. Bonato, M. Lozier, D. Mitsche, X. Péréz-Giménez and P. Prałat, The domination number of on-line social networks and random geometric graphs. Theory and Applications of Models of Computation. TAMC 2015, edited by R. Jain, S. Jain and F. Stephan. In Vol. 9076 of Lecture Notes in Computer Science. Springer, Cham (2015). [Google Scholar]
  3. A. Cannon and L. Cowen, Approximation algorithms for the class cover problem. 6th International Symposium on Artificial Intelligence and Mathematics (2000). [Google Scholar]
  4. E. Ceyhan and C.E. Priebe, The use of domination number of a random proximity catch digraph for testing spatial patterns of segregation and association. Stat. Prob. Lett. 73 (2005) 37–50. [CrossRef] [Google Scholar]
  5. E. Ceyhan, Extension of one-dimensional proximity regions to higher dimensions. Comp. Geom.-Theor. Appl. 43 (2010) 721–748. [CrossRef] [Google Scholar]
  6. E. Ceyhan, Spatial clustering tests based on domination number of a new family of random digraphs. Commun. Stat. A-Ther. 40 (2011) 1363–1395. [CrossRef] [Google Scholar]
  7. E. Ceyhan, Comparison of relative density of two random geometric digraph families in testing spatial clustering. TEST 23 (2014) 100–134. [CrossRef] [Google Scholar]
  8. J.G. DeVinney, The Class Cover Problem and its Applications in Pattern Recognition, Ph.D. dissertation, Johns Hopkins University (2003). [Google Scholar]
  9. J.G. DeVinney and C.E. Priebe, A new family of proximity graphs: class cover catch digraphs. Disc. Appl. Math. 154 (2006) 1975–1982. [CrossRef] [Google Scholar]
  10. J.G. DeVinney and J.C. Wierman, A SLLN for a one-dimensional class cover problem. Stat. Prob. Lett. 59 (2002) 425–435. [CrossRef] [Google Scholar]
  11. J.L. Doob, Stochastic Processes. Chapman & Hall, London (1953). [Google Scholar]
  12. C.K. Eveland, D.A. Socolinsky, C.E. Priebe and D.J. Marchette, A hierarchical methodology for one-class problems with skewed priors. J. Classif . 22 (2005) 17–48. [CrossRef] [Google Scholar]
  13. M. Haenggi, The secrecy graph and some of its properties. IEEE International Symposium on Information Theory (ISIT’08). Toronto, Canada (2008) 539–543. [Google Scholar]
  14. J.M. Hammersley and D.J.A. Welsh, First-passage percolation, subadditive processes, stochastic networks and generalized renewal theory, in Bernoulli-Bayes-Laplace Anniversary Volume, edited by L. LeCam and J. Neyman. Proceedings International Research Seminar, Statistical Laboratory, University of California, Berkeley. Springer Verlag (1965). [Google Scholar]
  15. T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs, Fundamentals. Marcel Dekker, Inc., New York (1998). [Google Scholar]
  16. J.F.C. Kingman, The ergodic theory of subadditive stochastic processes. J. R. Statist. Soc., Ser. B 30 (1968) 499–510. [Google Scholar]
  17. J.F.C. Kingman, Subadditive ergodic theory. Ann. Probab. 1 (1973) 883–909. [Google Scholar]
  18. S.R. Kulkarni, G. Lugosi and S.S. Vankatesh, Learning pattern classification – a survey. IEEE Trans. Info. Theory 44 (1998) 2178–2206. [CrossRef] [MathSciNet] [Google Scholar]
  19. D.J. Marchette and C.E. Priebe, Characterizing the scale dimension of a high-dimensional classification problem. Pattern Recogn. 36 (2003) 45–60. [CrossRef] [Google Scholar]
  20. A. Manukyan and E. Ceyhan, Classification of imbalanced data with a geometric digraph family. J. Mach. Learn. Res. 17 (2016) 1–40. [Google Scholar]
  21. O. Ore, Theory of Graphs. American Mathematical Society, Providence, R.I. (1962). [Google Scholar]
  22. M.D. Penrose and J.E. Yukich, Weak laws of large numbers in geometric probability. Ann. Appl. Probab. 13 (1993) 277–303. [Google Scholar]
  23. C.E. Priebe, D.J. Marchette, J.G. DeVinney and D. Socolinsky, Classification using class cover catch digraphs. J. Classif . 20 (2003) 3–23. [CrossRef] [Google Scholar]
  24. C.E. Priebe, J.L. Solka, D.J. Marchette and B.T. Clark, Class cover catch digraphs for latent class discovery in gene expression monitoring by DNA microarrays. Comp. Stat. Data An. on Visualization 43 (2003) 621–632. [CrossRef] [Google Scholar]
  25. W.T. Rhee, A matching problem and subadditive Euclidean functionals. Ann. Appl. Probab. 3 (1993) 794–801. [Google Scholar]
  26. A. Sasireka and A.H. Nandhu Kishore, Applications of dominating set of graph in computer networks. Int. J. Eng. Sci. Res. Technol. 3 (2014) 170–173. [Google Scholar]
  27. A. Sarkar and M. Haenggi, Percolation in the secrecy graph. Discr. Appl. Math. 161 (2013) 2120–2132. [CrossRef] [Google Scholar]
  28. R.T. Smythe, Multiparameter subadditive processes. Ann. Prob. 4 (1976) 772–782. [CrossRef] [Google Scholar]
  29. R.T. Smythe and J.C. Wierman, First-passage Percolation on the Square Lattice. Vol. 671 of Lect. Notes Math. (1978). [CrossRef] [Google Scholar]
  30. J.M. Steele, Subadditive Euclidean functionals and nonlinear growth in geometric probability. Ann. Probab. 4 (1981) 365–376. [Google Scholar]
  31. J.C. Wierman and P. Xiang, A general SLLN for a one-dimensional class cover problem. Stat. Prob. Lett. 78 (2008) 1110–1118. [CrossRef] [Google Scholar]
  32. P. Xiang and J.C. Wierman, A CLT for a one-dimensional class cover problem. Stat. Prob. Lett. 79 (2009) 223–233. [CrossRef] [Google Scholar]
  33. J.E. Yukich, Limit theorems in discrete stochastic geometry, Stochastic Geometry, Spatial Statistics and Random Fields, edited by E. Spodarev. In Vol. 2068 of Lecture Notes in Mathematics. Springer, Berlin, Heidelberg (2013). [Google Scholar]
  34. Y. Zhao, L. Kang and M.Y. Sohn, The algorithmic complexity of mixed domination in graphs. Theor. Comput. Sci. 412 (2011) 2387–2392. [CrossRef] [Google Scholar]

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