AVL tree (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "AVL tree" in English language version.

Last modified: 23:58:53, 29 June 2026 (UTC)

Ref.Un. Ref.Website

Global rank English rank

64worldcat.org

4^th place

61web.archive.org

1^st place

61wisc.edu

891^st place

533^rd place

54doi.org

2^nd place

32semanticscholar.org

15^th place

8^th place

22archive.org

6^th place

21stanford.edu

194^th place

182^nd place

21arxiv.org

49^th place

31^st place

11zhjwpku.com

low place

11stackexchange.com

4,114^th place

3,027^th place

11sidsen.azurewebsites.net

low place

11ams.org

434^th place

249^th place

11nist.gov

708^th place

742^nd place

11springer.com

182^nd place

172^nd place

11taylorfrancis.com

1,902^nd place

1,063^rd place

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

However, the balance information can be kept in the child nodes as one bit indicating whether the parent is higher by 1 or by 2; thereby higher by 2 cannot occur for both children. This way the AVL tree is a "rank balanced" tree, as coined by Haeupler, Sen and Tarjan. Haeupler, Bernhard; Sen, Siddhartha; Tarjan, Robert E. (2015), "Rank-balanced trees" (PDF), ACM Transactions on Algorithms, 11 (4): Art. 30, 26, doi:10.1145/2689412, MR 3361215, S2CID 1407290.

archive.org (Global: 6^th place; English: 6^th place)

Sedgewick, Robert (1983). "Balanced Trees". Algorithms. Addison-Wesley. p. 199. ISBN 0-201-06672-6.
Hubbard, John Rast (2000). Schaum's outline of theory and problems of data structures with Java. New York: McGraw-Hill. ISBN 0071378707. OCLC 48139308.

arxiv.org (Global: 49^th place; English: 31^st place)

Blelloch, Guy E.; Ferizovic, Daniel; Sun, Yihan (2016), "Just join for parallel ordered sets", Symposium on Parallel Algorithms and Architectures, ACM, pp. 253–264, arXiv:1602.02120, doi:10.1145/2935764.2935768, ISBN 978-1-4503-4210-0, S2CID 2897793.

doi.org (Global: 2^nd place; English: 2^nd place)

However, the balance information can be kept in the child nodes as one bit indicating whether the parent is higher by 1 or by 2; thereby higher by 2 cannot occur for both children. This way the AVL tree is a "rank balanced" tree, as coined by Haeupler, Sen and Tarjan. Haeupler, Bernhard; Sen, Siddhartha; Tarjan, Robert E. (2015), "Rank-balanced trees" (PDF), ACM Transactions on Algorithms, 11 (4): Art. 30, 26, doi:10.1145/2689412, MR 3361215, S2CID 1407290.
Blelloch, Guy E.; Ferizovic, Daniel; Sun, Yihan (2016), "Just join for parallel ordered sets", Symposium on Parallel Algorithms and Architectures, ACM, pp. 253–264, arXiv:1602.02120, doi:10.1145/2935764.2935768, ISBN 978-1-4503-4210-0, S2CID 2897793.
Mehlhorn, Kurt; Sanders, Peter (2008). Algorithms and Data Structures. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-540-77978-0. ISBN 978-3-540-77977-3.
Dinesh P. Mehta; Sartaj Sahni, eds. (2017-12-15). Handbook of Data Structures and Applications (2 ed.). New York: Chapman and Hall/CRC. doi:10.1201/9781315119335. ISBN 978-1-315-11933-5.

nist.gov (Global: 708^th place; English: 742^nd place)

xlinux.nist.gov

Paul E. Black (2015-04-13). "AVL tree". Dictionary of Algorithms and Data Structures. National Institute of Standards and Technology. Retrieved 2016-07-02.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

However, the balance information can be kept in the child nodes as one bit indicating whether the parent is higher by 1 or by 2; thereby higher by 2 cannot occur for both children. This way the AVL tree is a "rank balanced" tree, as coined by Haeupler, Sen and Tarjan. Haeupler, Bernhard; Sen, Siddhartha; Tarjan, Robert E. (2015), "Rank-balanced trees" (PDF), ACM Transactions on Algorithms, 11 (4): Art. 30, 26, doi:10.1145/2689412, MR 3361215, S2CID 1407290.
Blelloch, Guy E.; Ferizovic, Daniel; Sun, Yihan (2016), "Just join for parallel ordered sets", Symposium on Parallel Algorithms and Architectures, ACM, pp. 253–264, arXiv:1602.02120, doi:10.1145/2935764.2935768, ISBN 978-1-4503-4210-0, S2CID 2897793.

sidsen.azurewebsites.net (Global: low place; English: low place)

However, the balance information can be kept in the child nodes as one bit indicating whether the parent is higher by 1 or by 2; thereby higher by 2 cannot occur for both children. This way the AVL tree is a "rank balanced" tree, as coined by Haeupler, Sen and Tarjan. Haeupler, Bernhard; Sen, Siddhartha; Tarjan, Robert E. (2015), "Rank-balanced trees" (PDF), ACM Transactions on Algorithms, 11 (4): Art. 30, 26, doi:10.1145/2689412, MR 3361215, S2CID 1407290.

springer.com (Global: 182^nd place; English: 172^nd place)

link.springer.com

Mehlhorn, Kurt; Sanders, Peter (2008). Algorithms and Data Structures. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-540-77978-0. ISBN 978-3-540-77977-3.

stackexchange.com (Global: 4,114^th place; English: 3,027^th place)

cs.stackexchange.com

AVL trees are not weight-balanced? (meaning: AVL trees are not μ-balanced?)
Thereby: A Binary Tree is called $\mu$ -balanced, with $0\leq \mu \leq {\tfrac {1}{2}}$ , if for every node $N$ , the inequality
${\tfrac {1}{2}}-\mu \leq {\tfrac {|N_{l}|}{|N|+1}}\leq {\tfrac {1}{2}}+\mu$
holds and $\mu$ is minimal with this property. $|N|$ is the number of nodes below the tree with $N$ as root (including the root) and $N_{l}$ is the left child node of $N$ .

stanford.edu (Global: 194^th place; English: 182^nd place)

Pfaff, Ben (June 2004). "Performance Analysis of BSTs in System Software" (PDF). Stanford University.

taylorfrancis.com (Global: 1,902^nd place; English: 1,063^rd place)

Dinesh P. Mehta; Sartaj Sahni, eds. (2017-12-15). Handbook of Data Structures and Applications (2 ed.). New York: Chapman and Hall/CRC. doi:10.1201/9781315119335. ISBN 978-1-315-11933-5.

web.archive.org (Global: 1^st place; English: 1^st place)

Eric Alexander. "AVL Trees". Archived from the original on July 31, 2019.

wisc.edu (Global: 891^st place; English: 533^rd place)

pages.cs.wisc.edu

Eric Alexander. "AVL Trees". Archived from the original on July 31, 2019.

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Dixit, J. B. (2010). Mastering data structures through 'C' language. New Delhi, India: University Science Press, an imprint of Laxmi Publications Pvt. Ltd. ISBN 9789380386720. OCLC 939446542.
Brass, Peter (2008). Advanced data structures. Cambridge: Cambridge University Press. ISBN 9780511438202. OCLC 312435417.
Hubbard, John Rast (2000). Schaum's outline of theory and problems of data structures with Java. New York: McGraw-Hill. ISBN 0071378707. OCLC 48139308.
Weiss, Mark Allen (2006). Data structures and algorithm analysis in C++ (3rd ed.). Boston: Pearson Addison-Wesley. p. 145. ISBN 0-321-37531-9. OCLC 61278554.

zhjwpku.com (Global: low place; English: low place)

Adelson-Velsky, Georgy; Landis, Evgenii (1962). "An algorithm for the organization of information". Proceedings of the USSR Academy of Sciences (in Russian). 146: 263–266. English translation by Myron J. Ricci in Soviet Mathematics - Doklady, 3:1259–1263, 1962.

AVL tree (English Wikipedia)

ams.org (Global: 434th place; English: 249th place)

mathscinet.ams.org

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 49th place; English: 31st place)

doi.org (Global: 2nd place; English: 2nd place)

nist.gov (Global: 708th place; English: 742nd place)