Asymptotic distribution for the cost of linear probing hashing

Random Structures and Algorithms

Volumn 19, Issue 3-4, 2001, Pages 438-471

  Janson, Svante ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

Airy distribution; Brownian excursion area; Brownian motion; Hashing; Linear probing; Normal convergence; Parking problem; Poisson convergence; Stein's method

Indexed keywords

EID: 0035539866     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/rsa.10009     Document Type: Article

References (32)

1. D.J. Aldous and J. Pitman, The standard additive coalescent, Ann Probah 26 (1998), 1703-1726.
2. A.D. Barbour, L. Holst, and S. Janson, Poisson approximation, Oxford University Press, Oxford, 1992.
3. J. Bertoin, A fragmentation process connected to Brownian motion, Probab Theor Rel Fields 117 (2000), 289-301.
4. P. Billingsley, Convergence of probability measures, Wiley, New York, 1968.
5. P. Chassaing and S. Janson, A Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0, Ann Probab, to appear.
6. P. Chassaing and G. Louchard, Phase transition for parking blocks, Brownian excursion and coalescence, Rand Struct Alg, to appear.
7. P. Chassaing and J.F. Marckert, Parking functions, empirical processes and the width of rooted labelled trees. Electron J Combin 8 (2001), #R14.
8. A. Dvoretzky, J. Kiefer, and J. Wolfowitz, Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator, Ann Math Statist 27 (1956), 642-669.
9. P. Flajolet, P. Poblete, and A. Viola, On the analysis of linear probing hashing, Algorithmica 22 (1998), 490-515.
10. L. Holst, Two conditional limit theorems with applications, Ann Statist 7 (1979), 551-557.
11. L. Holst, Some conditional limit theorems in exponential families, Ann Probab 9 (1981), 818-830.
12. S. Janson, Moment convergence in conditional limit theorems, J Appl Probab 38 (2001), 421-437.
13. S. Janson, D.E. Knuth, T. Łuczak, and B. Pittel, The birth of the giant component, Rand Struct Alg 4 (1993), 233-358.
14. D.E. Knuth, Notes on "open" addressing. Unpublished notes, 1963. Available at http://www.wits.ac.za/helmut/first.ps
15. D.E. Knuth, The art of computer programming. Vol. 3: sorting and searching, 2nd ed., Addison-Wesley, Reading, MA, 1998.
16. D.E. Knuth, Linear probing and graphs, Algorithmica 22 (1998), 561-568.
17. V.F. Kolchin, Random mappings, Nauka, Moscow, 1984 (Russian). [English trans: Optimization software, New York, 1986.]
18. V.F. Kolchin, Random mappings, Nauka, Moscow, 1984 (Russian). [English trans: Optimization software, New York, 1986.]
19. A.G. Konheim and B. Weiss, An occupancy discipline and applications, SIAM J Appl Math 14 (1966), 1266-1274.
20. G. Louchard, Kac's formula, Lévy's local time and Brownian excursion, J Appl Probab 21 (1984), 479-499.
21. G. Louchard, The Brownian excursion area: a numerical analysis, Comput Math Appl 10 (1984), 413-417. Erratum: Comput Math Appl Part A 12 (1986), 375.
22. Yu.L. Pavlov, The asymptotic distribution of maximum tree size in a random forest. Teor. Verojatnost. i Primenen. 22 (1977), no. 3, 523-533 (Russian). [English trans: Theor Probab Appl 22 (3) (1977), 509-520.]
23. Yu.L. Pavlov, The asymptotic distribution of maximum tree size in a random forest. Teor. Verojatnost. i Primenen. 22 (1977), no. 3, 523-533 (Russian). [English trans: Theor Probab Appl 22 (3) (1977), 509-520.]
24. Yu.L. Pavlov, Random forests. Karelian Centre Russian Acad. Sci., Petrozavodsk, 1996 (Russian). [English trans: VSP, Zeist, The Netherlands, 2000.]
25. Yu.L. Pavlov, Random forests. Karelian Centre Russian Acad. Sci., Petrozavodsk, 1996 (Russian). [English trans: VSP, Zeist, The Netherlands, 2000.]
26. J. Pitman, Coalescent random forests, J Combin Theory A 85 (1999), 165-193.
27. J. Pitman and M. Yor, Arcsine laws and interval partitions derived from a stable subordinator, Proc London Math Soc (3) 65 (1992), 326-356.
28. D. Revuz and M. Yor, Continuous martingales and Brownian motion, 3rd ed., Springer, Berlin, 1999.
29. J. Spencer, Enumerating graphs and Brownian motion, Commun Pure Appl Math 50 (1997), 291-294.
30. L. Takács, A Bernoulli excursion and its various applications, Adv Appl Probab 23 (1991), 557-585.
31. W. Vervaat, A relation between Brownian bridge and Brownian excursion, Ann Probab 7 (1979), 143-149.
32. E.M. Wright, The number of connected sparsely edged graphs, J Graph Theor 1 (1977), 317-330.