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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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
Handbook of Mathematical Functions
(2018) · A Century of Excellence in MEASUREMENTS, STANDARDS, and TECHNOLOGY · doi:10.1201/9781351069397-39 · Cited by 9,062
Convergence of Probability Measures
Kingman, J. F. C., & Billingsley, P. (1969) · Revue de l'Institut International de Statistique / Review of the International Statistical Institute · doi:10.2307/1402124 · Cited by 6,812
On the Complexity of Finite Sequences
Lempel, A., & Ziv, J. (1976) · IEEE Transactions on Information Theory · doi:10.1109/tit.1976.1055501 · Cited by 2,717
Data Structures and Algorithms
(2003) · Series on software engineering and knowledge engineering · doi:10.1142/9789812791245 · Cited by 2,117
Data Structures and Algorithms
Wirth, N. (1984) · Scientific American · doi:10.1038/scientificamerican0984-60 · Cited by 1,418
Gani, J. (1969) · Technometrics · doi:10.1080/00401706.1969.10490702 · Cited by 1,023
Modular Functions and Dirichlet Series in Number Theory
Apostol, T. M. (1990) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-0999-7 · Cited by 966
Gonnet, G. H. (1984) · CERN Document Server (European Organization for Nuclear Research) · Cited by 448
Handbook of algorithms and data structures
Gonnet, G. H. (1984) · CERN Document Server (European Organization for Nuclear Research) · Cited by 436
Modular Functions and Dirichlet Series in Number Theory
Apostol, T. M. (1976) · Graduate Texts in Mathematics · doi:10.1007/978-1-4684-9910-0 · Cited by 435
Evolution of random search trees
Mahmoud, H. M. (1991) · Cited by 392
Q-ary collision resolution algorithms in random-access systems with free or blocked channel access
Mathys, P., & Flajolet, P. (1985) · IEEE Transactions on Information Theory · doi:10.1109/tit.1985.1057013 · Cited by 191
Digital Search Trees Revisited
Flajolet, P., & Sedgewick, R. (1986) · SIAM Journal on Computing · doi:10.1137/0215054 · Cited by 132
Paths in a random digital tree: limiting distributions
Pittel, B. G. (1986) · Advances in Applied Probability · doi:10.1017/s0001867800015603 · Cited by 115
File structures using hashing functions
Coffman, E. G., & Eve, J. K. (1970) · Communications of the ACM · doi:10.1145/362686.362693 · Cited by 100
Patricia tries again revisited
Szpankowski, W. (1990) · Journal of the ACM · doi:10.1145/96559.214080 · Cited by 84
Self-citationA diffusion limit for a class of randomly-growing binary trees
Aldous, D., & Shields, P. (1988) · Probability Theory and Related Fields · doi:10.1007/bf00318784 · Cited by 78
Some results on V-ary asymmetric tries
Szpankowski, W. (1988) · Journal of Algorithms · doi:10.1016/0196-6774(88)90039-9 · Cited by 65
Self-citationExact and asymptotic distributions in digital and binary search trees
Louchard, G. (1987) · RAIRO - Theoretical Informatics and Applications · doi:10.1051/ita/1987210404791 · Cited by 61
New results on the size of tries
Régnier, M., & Jacquet, P. (1989) · IEEE Transactions on Information Theory · doi:10.1109/18.42197 · Cited by 57
On the variance of the external path length in a symmetric digital trie
Kirschenhofer, P., Prodinger, H., & Szpankowski, W. (1989) · Discrete Applied Mathematics · doi:10.1016/0166-218x(89)90050-4 · Cited by 52
Self-citationOn some applications of formulae of Ramanujan in the analysis of algorithms
Kirschenhofer, P., & Prodinger, H. (1991) · Mathematika · doi:10.1112/s0025579300006409 · Cited by 43
Self-citationOn the balance property of Patricia tries: External path length viewpoint
Kirschenhofer, P., Prodinger, H., & Szpankowski, W. (1989) · Theoretical Computer Science · doi:10.1016/0304-3975(89)90115-1 · Cited by 35
Self-citationA note on growing binary trees
Konheim, A. G., & Newman, D. J. (1973) · Discrete Mathematics · doi:10.1016/0012-365x(73)90114-3 · Cited by 31
A characterization of digital search trees from the successful search viewpoint
Szpankowski, W. (1991) · Theoretical Computer Science · doi:10.1016/0304-3975(91)90050-c · Cited by 31
Self-citationFurther results on digital search trees
Kirschenhofer, P., & Prodinger, H. (1988) · Theoretical Computer Science · doi:10.1016/0304-3975(88)90023-0 · Cited by 22
Self-citation
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
- Nörlund N. E., 1954, Vorlesungen über Diferenzenrechnung
- 10.2307/1427240 · doi:10.2307/1427240
- W. Schachinger, Masters Thesis, Modulfunktionen und Analyse von Datenstrukturen, Diplomarbeit, TU Vienna, 1990
- 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
Self-citation
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
