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An empirical study of insertion and deletion in binary search trees

Jeffrey L. Eppinger
1983 Communications of the ACM  
Jeff Eppinger's current interests include distributed systems, database design, and analysis of algorithms.  ...  This paper presents an empirical study on the effect of applying random insertions and deletions to random binary search trees and analyzes results of experiments comparing asymmetric and symmetric deletion  ...  In this paper, T empirically examine the effect on IPL of applying pairs of insertions and deletions to binary trees.  ... 
doi:10.1145/358172.358183 fatcat:wgelx2upffhlhf66heqsq6cnxi

An empirical study of insertion and deletion in binary search trees

Jeffrey L. Eppinger
2018
[Knuth 73, Section 6.2.2] This paper presents an empirical study on the effect of applying random insertions and deletions to random binary search trees and analyzes results of experiments comparing asymmetric  ...  Section 2 describes the insertion and deletion algorithms used in this study and provides an overview of some of the previous work in this area.  ... 
doi:10.1184/r1/6603260.v1 fatcat:7xylzefcwrc7fjqamhig5fshlm

Fully Retroactive Priority Queues using Persistent Binary Search Trees

JoseWagner de Andrade Junior, Rodrigo Duarte Seabra
2020 Journal of Computer Science  
This work presents how to implement a data structure to a fully retroactive version of a priority queue through persistent self-balanced binary search trees in polylogarithmic time.  ...  The empirical analysis showed that the average performance of the proposed algorithm is better in terms of processing times than the other algorithms, despite the high constants in its complexity.  ...  Figure 5 presents the visual representation of an insertion operation in a binary search tree. The example shows the insertion of element 13 in the tree.  ... 
doi:10.3844/jcssp.2020.906.915 fatcat:ck6oxum5ezfkpcxkk6qh5qixn4

Deletion without rebalancing in multiway search trees

Siddhartha Sen, Robert E. Tarjan
2014 ACM Transactions on Database Systems  
Furthermore the amortized time for an insertion or deletion, excluding the search time, is O(1), and nodes are modified by insertions and deletions with a frequency that is exponentially small in their  ...  We show that the tree height remains logarithmic in the number of insertions, independent of the number of deletions.  ...  B − Trees In our discussion of multiway search trees we denote by m, d, n, and h, respectively, the number of insertions, the number of deletions, the current number of items in the tree, and the tree  ... 
doi:10.1145/2540068 fatcat:mrmcpox42bdvzaficjcbq3gyly

Deletion without Rebalancing in Multiway Search Trees [chapter]

Siddhartha Sen, Robert E. Tarjan
2009 Lecture Notes in Computer Science  
Furthermore the amortized time for an insertion or deletion, excluding the search time, is O(1), and nodes are modified by insertions and deletions with a frequency that is exponentially small in their  ...  We show that the tree height remains logarithmic in the number of insertions, independent of the number of deletions.  ...  B − Trees In our discussion of multiway search trees we denote by m, d, n, and h, respectively, the number of insertions, the number of deletions, the current number of items in the tree, and the tree  ... 
doi:10.1007/978-3-642-10631-6_84 fatcat:atfmazzflfeivilcm7bklhmxfa

A performance comparison of event calendar algorithms: An empirical approach

Kehsiung Chung, Janche Sang, Vernon Rego
1993 Software, Practice & Experience  
respond dynamically to dependent sequences of insertion and deletion requests.  ...  In contrast to previous studies based on the standard hold model for evaluation of performance statically, the proposed Markov hold model is more general and can be used to examine how different implementations  ...  Acknowledgement The authors gratefully acknowledge the help of Doug Jones in making this research effort possible. Thanks are also due to Jeff Kingston for his help.  ... 
doi:10.1002/spe.4380231005 fatcat:n2adekkpszfflkgu5b3x2rydoe

A trivial algorithm whose analysis isn't

Arne T. Jonassen, Donald E. Knuth
1978 Journal of computer and system sciences (Print)  
Knott proved a much deeper result [2] : "If 1z items are inserted into an initially empty binary tree, in random order, and if the first K items inserted are subsequently deleted by Hibbard's algorithm  ...  to binary search trees with three elements or less.  ...  On the other hand, Knott's empirical data in [2] indicate that the modified algorithm does indeed lead to an improvement when the trees are larger.  ... 
doi:10.1016/0022-0000(78)90020-x fatcat:i5atqt2ngnah3lvlpdtz6d5fiy

Quad trees a data structure for retrieval on composite keys

R. A. Finkel, J. L. Bentley
1974 Acta Informatica  
We define an optimized tree and present an algorithm to accomplish optimization in n log n time. Searching is guaranteed to be fast in optimized trees.  ...  An algorithm for retrieval within regions is presented along with data from empirical studies which imply that searching is reasonably efficient.  ...  Empirical studies with optimized trees of random nodes have shown that the TPL of trees after the treatment is roughly t 5 % lower than that obtained by straightforward insertion.  ... 
doi:10.1007/bf00288933 fatcat:3shovoqmk5fkbox7e5rzmlwjem

Page 7265 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
Larsen studies the version of multi-way trees called (a,b)-trees (which includes B-trees) with the operations in- sertion, deletion, and group insertion.  ...  Here we investigate the potential of suitably adapted binary search trees as competitors in this context.  ... 

Searching in Dynamic Tree-Like Partial Orders [chapter]

Brent Heeringa, Marius Cătălin Iordan, Louis Theran
2011 Lecture Notes in Computer Science  
The performance of our data structure is within an O(log w)-factor of optimal. Here w ≤ n is the width of the partialorder-a natural obstacle in searching a partial order.  ...  We define the Line-Leaf Tree, a linear-sized data structure that supports the operations: insert; delete; test membership; and predecessor.  ...  Andrew Lorenzen for his help in running the experiments discussed in Section 5.  ... 
doi:10.1007/978-3-642-22300-6_43 fatcat:4kztnemq7jcsphodulj5k5i3u4

On the average number of rebalancing operations in weight-balanced trees

Norbert Blum, Kurt Mehlhorn
1980 Theoretical Computer Science  
It is shown that the average number of rebalancing operations (rotations and double rotations) in weight-balanced trees is constant.  ...  Next we study the effect of insertion and deletions on root-balances. Lemma 1.  ...  A transaction is either an insertion or a deletion.  ... 
doi:10.1016/0304-3975(80)90018-3 fatcat:ytvaeuhex5ah7piakmecfa2dsi

An evaluation of self-adjusting binary search tree techniques

Jim Bell, Gopal Gupta
1993 Software, Practice & Experience  
Comparisons are made for various tree sizes, levels of key-access-frequency skewness and ratios of insertions and deletions to searches.  ...  Much has been said in praise of self-adjusting data structures, particularly self-adjusting binary search trees.  ...  For skewed key-access distributions, one may build an optimal binary search tree if the access frequencies are fixed and known in advance.  ... 
doi:10.1002/spe.4380230403 fatcat:jwllductsrdhre6n4pkrfim5fe

Contemporary Access Structures Under Mixed Workloads

A. Delis
1997 Computer journal  
In this paper, we compare experimentally two recently proposed self-adjusting access structures that can be used to organize data in such settings, namely, the Skip-List (SL) and the Binary B-Tree (BB-Tree  ...  Our experiments reveal the behaviour of SLs and BB-Trees under diverse environments and varying data requirements.  ...  This work was partially supported by the Center for Advanced Technology in Telecommunications (CATT) in Brooklyn, NY.  ... 
doi:10.1093/comjnl/40.4.183 fatcat:xdhrmhn5azacriigc7vwguadve

Multidimensional binary search trees used for associative searching

Jon Louis Bentley
1975 Communications of the ACM  
Various utility algorithms are developed; their proven average running times in an n record file are : insertion, O(log n); deletion of the root, 0 (n (k--1)/k) ; deletion of a random node, O(log n); and  ...  This paper develops the multidimensional binary search tree (or k-d tree, where k is the dimensionality of the search space) as a data structure for storage of information to be retrieved by associative  ...  into an initially empty k-d tree is the same as the probability of attaining that tree by random insertion into a one-dimensional binary search tree.  ... 
doi:10.1145/361002.361007 fatcat:aclosmj7hfcnfom5ux7k4ev34a

Engineering Top-Down Weight-Balanced Trees [article]

Lukas Barth, Dorothea Wagner
2019 arXiv   pre-print
Weight-balanced trees are a popular form of self-balancing binary search trees. Their popularity is due to desirable guarantees, for example regarding the required work to balance annotated trees.  ...  We provide an in-depth analysis and engineering of these top-down weight-balanced trees, demonstrating their superior performance.  ...  Insertion and Deletion in Bottom-Up Weight-Balanced Trees The first pass for insertion and deletion in bottom-up weight-balanced trees is performed as with unbalanced binary search trees.  ... 
arXiv:1910.07849v2 fatcat:54q2hsqhyrdy5erey72nxaqkoy
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