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Cited by 43Algorithms and Data CompressionAdvanced Combinatorial MathematicsOptimization and Search Problems

The DOI matches its Crossref record; 26 of the 26 references it cites were found in a registry or an index.

Digital Search Trees Again Revisited: The Internal Path Length Perspective

Kirschenhofer, Peter, Prodinger, Helmut, Szpankowski, Wojciech·1994·SIAM Journal on Computing
DOI 10.1137/s0097539790189368
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Abstract

This paper studies the asymptotics of the variance for the internal path length in a symmetric digital search tree under the Bernoulli model. This problem has been open until now. It is proved that the variance is asymptotically equal to $N \cdot 0.26600 + N \cdot \delta (\log _2 N)$, where N is the number of stored records and $\delta (x)$ is a periodic function of mean zero and a very small amplitude. This result completes a series of studies devoted to the asymptotic analysis of the variances of digital tree parameters in the symmetric case. In order to prove the previous result a number of nontrivial problems concerning analytic continuations and some others of a numerical nature had to be solved. In fact, some of these techniques are motivated by the methodology introduced in an influential paper by Flajolet and Sedgewick.

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Cites

Show all 26 references

Research works printed but not linked: 7

  1. 10.1007/978-1-4612-4530-8 · doi:10.1007/978-1-4612-4530-8
  2. P. Kirschenhofer, H. Prodinger, W. Szpankowski, G. X. Ritter, Digital search trees—further results on a fundamental data structure, Proceedings of IFIP 89, 1989, 443–447
  3. Knuth Donald E., 1973, The art of computer programming. Volume 3
  4. Nörlund N. E., 1954, Vorlesungen über Diferenzenrechnung
  5. 10.2307/1427240 · doi:10.2307/1427240
  6. W. Schachinger, Masters Thesis, Modulfunktionen und Analyse von Datenstrukturen, Diplomarbeit, TU Vienna, 1990
  7. Sedgewick R., 1988, Algorithms

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Metadata

Authors
Kirschenhofer, P., Prodinger, H., & Szpankowski, W.
Affiliations
  • Purdue University West Lafayette (US)
  • TU Wien (AT)
ORCID
Venue
SIAM Journal on Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
1994-06
Volume
23
Issue
3
Pages
598-616
ISSN
  • 0097-5397 (ISSN-L)
  • 1095-7111
DOI
10.1137/s0097539790189368
OpenAlex
W2129108235
Cited by
43
References
26
Citations by year
2026: 1 · 2020: 2 · 2015: 3 · 2013: 4 · 2012: 3
FWCI
4.12
Type
journal article
Language
en
Open access
closed
Locations
  • SIAM Journal on Computing (publishedVersion)
  • Purdue e-Pubs (Purdue University System) (submittedVersion)
Topics
  • Physical Sciences › Mathematics › Theoretical Computer Science › Algorithms and Data Compression
  • Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
  • Physical Sciences › Mathematics › Theoretical Computer Science › Optimization and Search Problems
Keywords
digital search trees, variance asymptotics, Bernoulli model, analytic continuation, digital trees

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