Analysis of some statistics for increasing tree families

Discrete Mathematics and Theoretical Computer Science

Volumn 6, Issue 2, 2004, Pages 437-460

  Panholzer, Alois ^a   Prodinger, Helmut ^b  

^a INSTITUT FÜR DISKRETE MATHEMATIK UND GEOMETRIE   (Austria)

^b UNIVERSITY OF THE WITWATERSRAND   (South Africa)

Author keywords

Ancestor tree size; Increasing trees; Steiner distance

Indexed keywords

BINARY CODES; COMPUTER SCIENCE; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PROBABILITY; RANDOM PROCESSES; STATISTICAL METHODS;

ANCESTOR-TREE SIZE; INCREASING TREES; STEINER-DISTANCE;

TREES (MATHEMATICS);

EID: 11144294146     PISSN: 13658050     EISSN: 13658050     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. D. Aldous, The continuum random tree II: an overview, Stochastic analysis (Prod., Durham, 1990), 23-70, London Math. Soc. Lecture Note Ser. 167, 1991.
2. F. Bergeron, Ph. Flajolet and B. Salvy, Varieties of Increasing Trees, Lecture Notes in Computer Science 581, 24-48, 1992.
3. B. Bollobás and O. Riordan, Mathematical results on scale-free random graphs, in: Handbook of graphs and networks, 1-34, Wiley, Weinheim, 2003.
4. P. Dankelmann, O. R. Oellermann and H. C. Swart, The Average Steiner Distance of a Graph, Journal of Graph Theory 22, 15-22, 1996.
5. L. Devroye and R. Neininger, Distances and finger search in random binary search trees, SIAM Journal on Computing 33, 647-658, 2004.
6. Ph. Flajolet and A. Odlyzko, Singularity Analysis of Generating Functions, SIAM Journal on Discrete Mathematics 3, 216-240, 1990.
7. Ph. Flajolet and R. Sedgewick, An Introduction to the Analysis of Algorithms, Addison-Wesley, Reading, 1996.
8. R. van der Hofstad, G. Hooghiemstra and P. Van Mieghem, On the Covariance of the Level Sizes in Random Recursive Trees, Random Structures & Algorithms 20, 519-539, 2002.
9. H.-K. Hwang, On Convergence Rates in the Central Limit Theorems for Combinatorial Structures, European Journal of Combinatorics 19, 329-343, 1998.
10. H. Mahmoud and R. Neininger, Distribution of Distances in Random Binary Search Trees, The Annals of Applied Probability, 13, 253-276, 2002.
11. H. Mahmoud and R. Smythe, A Survey of Recursive Trees, Theoretical Probability and Mathematical Statistics 51, 1-27, 1995.
12. A. Meir and J. W. Moon, On the altitude of nodes in random trees, Canadian Journal of Mathematics 30, 997-1015, 1978.
13. K. Morris, A. Panholzer and H. Prodinger, On some parameters in heap ordered trees, Combinatorics, Probability and Computing, accepted for publication, 2002.
14. A. Panholzer, The distribution of the size of the ancestor-tree and of the induced spanning subtree for random trees, Random Structures & Algorithms 25, 179-207, 2004.
15. A. Panholzer and H. Prodinger, Spanning tree size in random binary search trees, The Annals of Applied Probability 14, 718-733, 2004.
16. H. Prodinger, Multiple Quickselect - Hoare's Find algorithm for several elements, Information Processing Letters 56, 123-129, 1995.