Download this PDF file Fullscreen Fullscreen Off
References
- Aldous, David. Asymptotic fringe distributions for general families of random trees. Ann. Appl. Probab. 1 (1991), no. 2, 228--266. MR1102319
- Aldous, David. The continuum random tree. II. An overview. Stochastic analysis (Durham, 1990), 23--70, London Math. Soc. Lecture Note Ser., 167, Cambridge Univ. Press, Cambridge, 1991. MR1166406
- Bennies, Jörgen; Kersting, Götz. A random walk approach to Galton-Watson trees. J. Theoret. Probab. 13 (2000), no. 3, 777--803. MR1785529
- Bóna, Miklós. $k$-Protected vertices in binary search trees. Adv. in Appl. Math. 53 (2014), 1--11. MR3149690
- Cheon, Gi-Sang; Shapiro, Louis W. Protected points in ordered trees. Appl. Math. Lett. 21 (2008), no. 5, 516--520. MR2402845
- Devroye, Luc. Branching processes and their applications in the analysis of tree structures and tree algorithms. Probabilistic methods for algorithmic discrete mathematics, 249--314, Algorithms Combin., 16, Springer, Berlin, 1998. MR1678582
- Devroye, Luc. Limit laws for sums of functions of subtrees of random binary search trees. SIAM J. Comput. 32 (2002/03), no. 1, 152--171. MR1954858
- Devroye, Luc; Fawzi, Omar; Fraiman, Nicolas. Depth properties of scaled attachment random recursive trees. Random Structures Algorithms 41 (2012), no. 1, 66--98. MR2943427
- Drmota, Michael. Random trees. An interplay between combinatorics and probability. SpringerWienNewYork, Vienna, 2009. xviii+458 pp. ISBN: 978-3-211-75355-2 MR2484382
- Du, Rosena R. X.; Prodinger, Helmut. Notes on protected nodes in digital search trees. Appl. Math. Lett. 25 (2012), no. 6, 1025--1028. MR2902374
- Gaither, Jeffrey; Homma, Yushi; Sellke, Mark; Ward, Mark Daniel. On the number of 2-protected nodes in tries and suffix trees. 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), 381--397, Discrete Math. Theor. Comput. Sci. Proc., AQ, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2012. MR2957345
- Jeffrey Gaither and Mark Daniel Ward, The variance of the number of 2-protected nodes in a trie. phProceedings, Tenth Workshop on Analytic Algorithmics and Combinatorics, ANALCO 2013 (New Orleans 2013), SIAM, Philadephia, PA, 2013, 43--51.
- Cecilia Holmgren and Svante Janson, Limit laws for functions of fringe trees for binary search trees and recursive trees. In preparation.
- Janson, Svante. Simply generated trees, conditioned Galton-Watson trees, random allocations and condensation. Probab. Surv. 9 (2012), 103--252. MR2908619
- Kennedy, Douglas P. The Galton-Watson process conditioned on the total progeny. J. Appl. Probability 12 (1975), no. 4, 800--806. MR0386042
- Mahmoud, Hosam M.; Ward, Mark Daniel. Asymptotic distribution of two-protected nodes in random binary search trees. Appl. Math. Lett. 25 (2012), no. 12, 2218--2222. MR2967819
- Hosam H. Mahmoud and Mark Daniel Ward, Asymptotic properties of protected nodes in random recursive trees. Preprint, 2013.
- Mansour, Toufik. Protected points in $k$-ary trees. Appl. Math. Lett. 24 (2011), no. 4, 478--480. MR2749730
- Smythe, Robert T.; Mahmoud, Hosam M. A survey of recursive trees. (Ukrainian) ; translated from Teor. Ĭmovīr. Mat. Stat. No. 51 (1994), 1--29 Theory Probab. Math. Statist. No. 51 (1995), 1--27 (1996) MR1445048

This work is licensed under a Creative Commons Attribution 3.0 License.