References
- L. Devroye and S. Janson, Protected nodes and fringe subtrees in some random trees, Electron. Commun. Probab, 19 (2014), 1–10.
- M. Drmota, Random trees: An interplay between combinatorics and probability, SpringerWienNewYork, Vienna, 2009.10.1007/978-3-211-75357-6
- M. Drmota and W. Szpankowski, The expected profile of digital search trees, J. Combin. Theory Ser. A, 118 (2011), 1939–1965.10.1016/j.jcta.2011.04.001
- M. Drmota, M. Fuchs, H.K. Hwang and R. Neininger, Node profiles of symmetric digital search trees, https://arxiv.org/abs/1711.06941, submitted (2020), 41 pages.
- P. Flajolet, X. Gourdon and P. Dumas, Mellin transforms and asymptotics: harmonic sums, Theoret. Comput. Sci., 144 (1995), 3–58,.
- P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press, 2009.10.1017/CBO9780511801655
- M. Fuchs, C.-K. Lee and G.-R. Yu, On 2-protected nodes in random digital trees, Theor. Comput. Sci., 622 (2016), 111–122.10.1016/j.tcs.2016.02.007
- P. Jacquet and W. Szpankowski, Analytical depoissonization and its applications, Theoret. Comput. Sci. 201 (1998), 1–62.10.1016/S0304-3975(97)00167-9
- M. Javanian, Protected node profile of tries, Discrete Mathematics & Theoretical Computer Science, 20 (2018), 1–20.
- M. Javanian, R. Imany Nabiyyi and J. Toofanpour, Protected node profile in recursive trees, Theory of Probability and Its Applications, accepted, 2021.
- R. Kazemi and M. Vahidi-Asl, The variance of the profile in digital search trees, Discrete Math. Theor. Comput. Sci., 13 (2011), 21–38.
- D.E. Knuth, The art of computer programming, Volume 3: sorting and searching, Addison Wesley Longman Publishing Co., Inc. Redwood City, CA, USA, 1998.
- Du. Rosena R.X. and H. Prodinger, Notes on protected nodes in digital search trees, Appl. Math. Lett., 25 (2012), 1025–1028.10.1016/j.aml.2011.11.017
- G. Louchard, Exact and asymptotic distributions in digital and binary search trees, RAIRO Theor. Inform. Appl., 21 (1987), 479–495.10.1051/ita/1987210404791
- H. M. Mahmoud, Evolution of random search trees, John Wiley & Sons Inc., New York, 1992.
- A. Magner, W. Szpankowski, Profile of PATRICIA tries, Algorithmica, 80 (2018), 331–397.10.1007/s00453-016-0261-5
- G. Park, H.-K. Hwang, P. Nicodème and W. Szpankowski, Profile of tries, SIAM J. Comput., 38 (2009), 1821–1880.10.1137/070685531
- W. Szpankowski, Average case analysis of algorithms on sequences, Wiley, New York, 2001.10.1002/9781118032770
- V. M. Zolotarev, Approximation of the distributions of sums of independent random variables with values in infinite-dimensional spaces, Theory Probab. Appl., 21 (1976), 721–737.10.1137/1121086
- V. M. Zolotarev, Ideal metrics in the problem of approximating the distributions of sums of independent random variables, Theory Probab. Appl., 22 (1977), 433–339,.10.1137/1122056