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
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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“who prove that a^[W{n)] login where C = 0.26600 (to five significant places)”
From A statistical test suite for random and pseudorandom number generators for cryptographic applications (2000) · cites this paper as Kirschenhofer, Prodinger, and Szpankowski (1994)
Citations
Cites
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Research works printed but not linked: 7
- 10.1007/978-1-4612-4530-8 · doi:10.1007/978-1-4612-4530-8
- 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
- Knuth Donald E., 1973, The art of computer programming. Volume 3
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- Sedgewick R., 1988, Algorithms
Cited by
Rukhin, A., Sota, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., et al. (2000) · doi:10.6028/nist.sp.800-22 · Cited by 1,867
TestU01: A C library for empirical testing of random number generators
L'Ecuyer, P., & Simard, R. (2007) · ACM Transactions on Mathematical Software · doi:10.1145/1268776.1268777 · Cited by 1,014
Analytical depoissonization and its applications
Jacquet, P., & Szpankowski, W. (1998) · Theoretical Computer Science · doi:10.1016/s0304-3975(97)00167-9 · Cited by 164
Self-citationA general limit theorem for recursive algorithms and combinatorial structures
Neininger, R., & Rüschendorf, L. (2004) · The Annals of Applied Probability · doi:10.1214/aoap/1075828056 · Cited by 141
Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
Jacquet, P., & Szpankowski, W. (1995) · Theoretical Computer Science · doi:10.1016/0304-3975(94)00298-w · Cited by 106
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Metadata
- Authors
- Kirschenhofer, P., Prodinger, H., & Szpankowski, W.
- Affiliations
- Purdue University West Lafayette (US)
- TU Wien (AT)
- Venue
- SIAM Journal on Computing
- Published
- 1994-06
- Volume
- 23
- Issue
- 3
- Pages
- 598-616
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- 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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- CoChat. (2026). Citation check: Digital Search Trees Again Revisited: The Internal Path Length Perspective. https://app.cochat.ai/papers/10.1137/s0097539790189368
- The paper
- Kirschenhofer, P., Prodinger, H., & Szpankowski, W. (1994). Digital Search Trees Again Revisited: The Internal Path Length Perspective. SIAM Journal on Computing. https://doi.org/10.1137/s0097539790189368
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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