Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-25T14:11:33.784Z Has data issue: false hasContentIssue false

Individual Displacements in Hashing with Coalesced Chains

Published online by Cambridge University Press:  01 November 2008

SVANTE JANSON*
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, S-751 06 Uppsala, Sweden (e-mail: svante.janson@math.uu.sehttp://www.math.uu.se/~svante/)

Abstract

We study the asymptotic distribution of the displacements in hashing with coalesced chains, for both late-insertion and early-insertion. Asymptotic formulas for means and variances follow. The method uses Poissonization and some stochastic calculus.

Type
Paper
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Athreya, K. B. and Ney, P. E. (1972) Branching Processes, Springer, Berlin.CrossRefGoogle Scholar
[2]Billingsley, P. (1968) Convergence of Probability Measures, Wiley, New York.Google Scholar
[3]Chen, W. C. and Vitter, J. S. (1983) Analysis of early-insertion standard coalesced hashing. SIAM J. Comput. 12 667676.CrossRefGoogle Scholar
[4]Janson, S. (2005) Individual displacements for linear probing hashing with different insertion policies. ACM Trans. Algorithms 1 177213.CrossRefGoogle Scholar
[5]Knott, G. D. (1984) Direct-chaining with coalescing lists. J. Algorithms 5 721.CrossRefGoogle Scholar
[6]Knuth, D. E. (1998) The Art of Computer Programming, Vol. 3: Sorting and Searching, 2nd edn, Addison-Wesley, Reading, MA.Google Scholar
[7]Protter, P. E. (2004) Stochastic Integration and Differential Equations, 2nd edn, Springer, Berlin.Google Scholar
[8]Viola, A. (2005) Exact distributions of individual displacements in linear probing hashing. ACM Trans. Algorithms 1 214242.CrossRefGoogle Scholar
[9]Vitter, J. S. and Chen, W. C. (1987) Design and Analysis of Coalesced Hashing, International Series of Monographs on Computer Science, Oxford University Press, New York.Google Scholar
[10]Williams, F. A. (1959) Handling identifiers as internal symbols in language processors. Comm. Assoc. Comput. Mach. l2 2124.Google Scholar