Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T01:14:43.605Z Has data issue: false hasContentIssue false
  • English
  • Français

Average-Case Analysis of Cousins in m-ary Tries

Part of: Theory of data Graph theory Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Hosam M. Mahmoud  and
Mark Daniel Ward
Hosam M. Mahmoud*
Affiliation:
The George Washington University
Mark Daniel Ward*
Affiliation:
Purdue University
*
∗Postal address: Department of Statistics, The George Washington University, 2140 Pennsylvania Avenue NW, Washington, DC 20052, USA. Email address: [email protected]
∗∗Postal address: Department of Statistics, Purdue University, 150 North University Street, West Lafayette, IN 47907-1451, USA. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the average similarity of random strings as captured by the average number of ‘cousins’ in the underlying tree structures. Analytical techniques including poissonization and the Mellin transform are used for accurate calculation of the mean. The string alphabets we consider are m-ary, and the corresponding trees are m-ary trees. Certain analytic issues arise in the m-ary case that do not have an analog in the binary case.

Keywords

Analysis of algorithmsrandom treerecurrenceMellin transformpoissonizationcombinatorics on wordssimilarity of strings

MSC classification

Secondary: 05C05: Trees 60C05: Combinatorial probability 68P05: Data structures 68P10: Searching and sorting 68P20: Information storage and retrieval
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 888 - 900
Copyright
Copyright © Applied Probability Trust 2008 

References

[1] Aguech, R., Lasmar, N. and Mahmoud, H. (2006). Distances in random digital search trees. Acta Informatica 43, 243–264.CrossRefGoogle Scholar
[2] Aguech, R., Lasmar, N. and Mahmoud, H. (2006). Limit distribution of distances in biased random tries. J. App. Prob. 43, 1–14.CrossRefGoogle Scholar
[3] Briandais, R. D. L. (1959). File searching using variable length keys. In Proc. Western Joint Comput. Conf., AFIPS, San Francisco, CA, pp. 295–298.Google Scholar
[4] Bruss, F. T., Louchard, G. and Ward, M. D. (2008). Injecting unique minima into random sets. To appear in ACM Trans. Algorithms. Google Scholar
[5] Christophi, C. and Mahmoud, H. (2005). The oscillatory distribution of distances in random tries. Ann. Appl. Prob. 15, 1536–1564.CrossRefGoogle Scholar
[6] Christophi, C. and Mahmoud, H. (2008). On climbing tries. Prob. Eng. Inf. Sci. 22, 133–149.CrossRefGoogle Scholar
[7] Drmota, M., Reznik, Y., Savari, S. and Szpankowski, W. (2008). Analysis of variable-to-fixed length codes. Submitted.Google Scholar
[8] Fagin, R., Nievergelt, J., Pippenger, N. and Strong, H. (1979). Extendible hashing—a fast access method for dynamic files. ACM Trans. Database Systems 4, 315–344.CrossRefGoogle Scholar
[9] Flajolet, P. and Sedgewick, R. (1995). Mellin transforms and asymptotics: finite differences and Rice's integrals. Theoret. Comput. Sci. 144, 101–124.CrossRefGoogle Scholar
[10] Flajolet, P., Gourdon, X. and Dumas, P. (1995). Mellin transforms and asymptotics: harmonic sums. Theoret. Comput. Sci. 144, 3–58.CrossRefGoogle Scholar
[11] Fredkin, E. (1960). Trie memory. Commun. ACM 3, 490–499.CrossRefGoogle Scholar
[12] Henrici, P. (1986). Applied and Computational Complex Analysis. John Wiley, New York.Google Scholar
[13] Jacquet, P. and Szpankowski, W. (1998). Analytical depoissonization and its applications. Theoret. Comput. Sci. 201, 1–62.CrossRefGoogle Scholar
[14] Knuth, D. E. (1998). The Art of Computer Programming, Vol. 3, 2nd edn. Addison-Wesley, Reading, MA.Google Scholar
[15] Korevaar, J. (2002). A century of complex Tauberian theory. Bull. Amer. Math. Soc. (N. S.) 39, 475–531.CrossRefGoogle Scholar
[16] Schachinger, W. (1992). Beitrage zur analyse von datenstrkturen zur digitalen suche. , Technical University of Vienna.Google Scholar
[17] Schachinger, W. (2000). Limiting distributions for the costs of partial match retrievals in multidimensional tries. Random Structures Algorithms 17, 428–459.3.0.CO;2-6>CrossRefGoogle Scholar
[18] Szpankowski, W. (2001). Average Case Analysis of Algorithms on Sequences. John Wiley, New York.CrossRefGoogle Scholar