On the internal path length of d-dimensional quad trees

Random Structures and Algorithms

Volumn 15, Issue 1, 1999, Pages 25-41

  Neininger, Ralph ^a   Rüschendorf, Ludger ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Analysis of algorithms; Contraction method; M ary search trees; Multidimensional data structure; Quad trees; Split trees

Indexed keywords

EID: 0039346499     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199908)15:1<25::AID-RSA2>3.0.CO;2-R     Document Type: Article

References (18)

1. D. Aldous, "Probability distributions on cladograms," Random discrete structures, The IMA Volumes in Mathematics and Its Applications, Vol. 76, pp. 1-18, D. Aldous and R. Pemantle (Editors), Springer-Verlag, New York, 1996.
2. L. Devroye, A note on the expected height of binary search trees, J ACM 33 (1986), 489-498.
3. L. Devroye, Branching processes in the analysis of the heights of trees, Acta Inform 24 (1987), 277-298.
4. L. Devroye, Universal limit laws for depths in random trees, SIAM J Comput 28 (1999), 409-432.
5. L. Devroye and L. Laforest, An analysis of random n-dimensional quad trees, SIAM J Comput 19 (1990), 821-832.
6. R.P. Dobrow and J.A. Fill, Total path length for random recursive trees, Combinatorics, Probab Comput In press.
7. R.A. Finkel and J.L. Bentley, Quad trees, a data structure for retrieval on composite keys, Acta Inform 4 (1974), 1-9.
8. P. Flajolet, G. Gonnet, C. Puech, and J.M. Robson, Analytic variations on quadtrees, Algorithmica 10 (1993), 473-500.
9. P. Flajolet, G. Labelle, L. Laforest, and B. Salvy, Hypergeometrics and the cost structure of quadtrees, Random Struct Alg 7 (1995), 117-144.
10. P. Flajolet, and T. Lafforgue, Search costs in quadtrees and singularity perturbation asymptotics, Discrete Computat Geom 12 (1994), 151-175.
11. H. Mahmoud, On the average internal path length of m-ary search trees, Acta Inform 23 (1986), 111-117.
12. H. Mahmoud, Evolution of random search trees, John Wiley, New York, 1992.
13. S.T. Rachev, The Monge-Kantorovich mass transference problem and its stochastic applications, Theory Probab Appl 29 (1984), 647-676.
14. S.T. Rachev and L. Rüschendorf, Probability metrics and recursive algorithms, Adv Appl Probab 27, (1995) 770-799.
15. M. Régnier, A limiting distribution for Quicksort, RAIRO, Theoret Inform Appl 23 (1989), 335-343.
16. U. Rösler, A limit theorem for "Quicksort," RAIRO, Theoret Inform Appl 25 (1991), 85-100.
17. U. Rösler, A fixed point theorem for distributions, Stoch Proc Appl 42 (1992), 195-214.
18. U. Rösler, On the analysis of stochastic divide and conquer algorithms, preprint, 1998.