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Performance of height-balanced trees

Authors:

P. L. Karlton,

S. H. Fuller,

R. E. Scroggs, and

E. B. KaehlerAuthors Info & Claims

Communications of the ACM, Volume 19, Issue 1

Pages 23 - 28

https://doi.org/10.1145/359970.359989

Published: 01 January 1976 Publication History

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Abstract

This paper presents the results of simulations that investigate the performance of height-balanced (HB[k]) trees. It is shown that the only statistic of HB[1] trees (AVL trees) that is a function of the size of the tree is the time to search for an item in the tree. For sufficiently large trees, the execution times of all procedures for maintaining HB[1] trees are independent of the size of the tree. In particular, an average of .465 restructures are required per insertion, with an average of 2.78 nodes revisited to restore the HB[1] property; an average of .214 restructures are required per deletion, with an average of 1.91 nodes revisited to restore the HB[1] property. Moreover, the execution times of procedures for maintaining HB[k] trees, for k > 1, are also independent of the size of the tree except for the average number of nodes revisited on a delete operation in order to restore the HB[k] property on traceback. The cost of maintaining HB[k] trees drops sharply as the allowable imbalance (k) increases. Both analytical and experimental results that show the cost of maintaining HB[k] trees as a function of k are discussed.

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Cited By

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Levin M(2022)Balanced Clustering with a Tree over ClustersJournal of Communications Technology and Electronics10.1134/S106422692113005266:S1(S23-S34)Online publication date: 24-Mar-2022
https://doi.org/10.1134/S1064226921130052
Levin M(2018)On Balanced Clustering (Indices, Models, Examples)Journal of Communications Technology and Electronics10.1134/S106422691712010562:12(1506-1515)Online publication date: 27-Feb-2018
https://doi.org/10.1134/S1064226917120105
Peng XWang ZHan FSong GDing S(2018)A novel time-event-driven algorithm for simulating spiking neural networks based on circular arrayNeurocomputing10.1016/j.neucom.2018.02.085292(121-129)Online publication date: May-2018
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Index Terms

Performance of height-balanced trees

Index terms have been assigned to the content through auto-classification.

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Published In

Communications of the ACM Volume 19, Issue 1

Jan. 1976

45 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/359970

Editor:
Robert L. Ashenhurst
Univ. of Chicago, Chicago, IL

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1976

Published in CACM Volume 19, Issue 1

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Levin M(2022)Balanced Clustering with a Tree over ClustersJournal of Communications Technology and Electronics10.1134/S106422692113005266:S1(S23-S34)Online publication date: 24-Mar-2022
https://doi.org/10.1134/S1064226921130052
Levin M(2018)On Balanced Clustering (Indices, Models, Examples)Journal of Communications Technology and Electronics10.1134/S106422691712010562:12(1506-1515)Online publication date: 27-Feb-2018
https://doi.org/10.1134/S1064226917120105
Peng XWang ZHan FSong GDing S(2018)A novel time-event-driven algorithm for simulating spiking neural networks based on circular arrayNeurocomputing10.1016/j.neucom.2018.02.085292(121-129)Online publication date: May-2018
https://doi.org/10.1016/j.neucom.2018.02.085
Ziviani NTompa F(2016)A Look at Symmetric Binary B-TreesINFOR: Information Systems and Operational Research10.1080/03155986.1982.1173184920:2(65-81)Online publication date: 25-May-2016
https://doi.org/10.1080/03155986.1982.11731849
Saikkonen RSoisalon-Soininen E(2015)Cache-Sensitive Memory Layout for Dynamic Binary TreesThe Computer Journal10.1093/comjnl/bxv09059:5(630-649)Online publication date: 4-Nov-2015
https://doi.org/10.1093/comjnl/bxv090
Raman I(2014)On counting and embedding a subclass of height-balanced treesModelling and Simulation in Engineering10.1155/2014/7489412014(34-34)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.1155/2014/748941
Fu ZLandsiedel OAlmgren MPapatriantafilou M(2014)Managing your trees: Insights from a metropolitan-scale low-power wireless network2014 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)10.1109/INFCOMW.2014.6849310(664-669)Online publication date: Apr-2014
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Štrbac-Savić STomašević MIvanović MBudimac Z(2012)Comparative performance evaluation of the AVL and red-black treesProceedings of the Fifth Balkan Conference in Informatics10.1145/2371316.2371320(14-19)Online publication date: 16-Sep-2012
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Tsakalidis A(2011)Rebalancing operations for deletions in AVL-treesRAIRO. Informatique théorique10.1051/ita/198519040323119:4(323-329)Online publication date: 8-Jan-2011
https://doi.org/10.1051/ita/1985190403231
Olivié H(2011)A new class of balanced search trees : half-balanced binary search tressRAIRO. Informatique théorique10.1051/ita/198216010051116:1(51-71)Online publication date: 8-Jan-2011
https://doi.org/10.1051/ita/1982160100511
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A generalization of AVL trees

Rank-Balanced Trees

On the Height of Multidimensional Height-Balanced Trees

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