Amortized rotation cost in AVL trees

Amani, Mahdi; Lai, Kevin A.; Tarjan, Robert E.

doi:10.1016/j.ipl.2015.12.009

Cited by 7 publications

(5 citation statements)

References 3 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This property implies that if we construct an AVL Tree of height h from an initially empty tree, then the nodes of the final tree can be divided into groups based on the period they were added as leaves. We note that this property is a more explicit formulation of the result in [ALT16], that proves that an n-node AVL tree can be constructed using n inserts.…”

Section: Our Contributionsmentioning

confidence: 63%

“…There has been renewed interest in AVL tree with the development of new AVL variantsrank-balanced tree [HST09] and ravl tree [ST10], and the analysis of AVL tree performance with respect to the number of rotations [ALT16]. Very recently, an open problem posed in [GV20] asks for an alternative analysis of the height of AVL tree using a potential function.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Tale of Two Trees: New Analysis for AVL Tree and Binary Heap

L.¹,

Samaniego²,

Jacildo³

et al. 2020

Preprint

View full text Add to dashboard Cite

In this paper, we provide new insights and analysis for the two elementary tree-based data structures -the AVL tree and binary heap. We presented two simple properties that gives a more direct way of relating the size of an AVL tree and the Fibonacci recurrence to establish the AVL tree's logarithmic height. We then give a potential function-based analysis of the bottom-up heap construction to get a simpler and tight bound for its worst-case running-time.

show abstract

Section: Our Contributionsmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

A Tale of Two Trees: New Analysis for AVL Tree and Binary Heap

L.¹,

Samaniego²,

Jacildo³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The deletions of AVL trees is more complicated and Θ(log n) rotations can be applied on every deletion. Amani et al [ALT16] recently showed that there exists such a sequence of 3n intermixed insertions and deletions on an initially empty AVL tree that takes Θ(n log n) rotations. This instance indicates that the classic implementation of AVL trees has an I/O cost Q = Θ(ω log n) per deletion in the worst case.…”

Section: I/o Cost On Bstsmentioning

confidence: 99%

Algorithmic Building Blocks for Asymmetric Memories

Gu,

Sun,

Blelloch

2018

Preprint

View full text Add to dashboard Cite

The future of main memory appears to lie in the direction of new non-volatile memory technologies that provide strong capacity-to-performance ratios, but have write operations that are much more expensive than reads in terms of energy, bandwidth, and latency. This asymmetry can have a significant effect on algorithm design, and in many cases it is possible to reduce writes at the cost of reads. In this paper we study which algorithmic techniques are useful in designing practical write-efficient algorithms. We focus on several fundamental algorithmic building blocks including unordered set/map implemented using hash tables, ordered set/map implemented using various binary search trees, comparison sort, and graph traversal algorithms including breadth-first search and Dijkstra's algorithm. We introduce new algorithms and implementations that can reduce writes, and analyze the performance experimentally using a software simulator. Finally we summarize interesting lessons and directions in designing write-efficient algorithms.

show abstract

“…Several variations of the binary tree structure have been conceived, such as binary search trees, red-black trees [10], AVL trees [1], B-trees [3], and so on. Binary trees are often used as auxiliary data structures in other research endeavors, both practical (e.g., [18,15]) and theoretical (e.g., [16,14]), but occasionally are the subject of the research itself (e.g., [2]). …”

Section: Introductionmentioning

confidence: 99%

“…Likewise, the clockwise roll of a binary tree, abbreviated as CW(), is de ined as in De inition 2: (2) Similarly, upon CW(), the inorder traversal of the original tree is identical to the preorder traversal of the tree obtained by the clockwise roll, and the postorder traversal of the original tree is identical to the inorder traversal of the tree obtained by the clockwise roll.…”

Section: Introductionmentioning

confidence: 99%

Space Complexity Analysis of the Binary Tree Roll Algorithm

Božinovski

Tanev

Stojcevska

et al. 2017

JITA

View full text Add to dashboard Cite

This paper presents the space complexity analysis of the Binary Tree Roll algorithm. The space complexity is analyzed theoretically and the results are then confi rmed empirically. The theoretical analysis consists of determining the amount of memory occupied during the execution of the algorithm and deriving functions of it, in terms of the number of nodes of the tree n, for the worst -and best-case scenarios. The empirical analysis of the space complexity consists of measuring the maximum and minimum amounts of memory occupied during the execution of the algorithm, for all binary tree topologies with the given number of nodes. The space complexity is shown, both theoretically and empirically, to be logarithmic in the best case and linear in the worst case, whereas its average case is shown to be dominantly logarithmic.

show abstract

Amortized rotation cost in AVL trees

Cited by 7 publications

References 3 publications

A Tale of Two Trees: New Analysis for AVL Tree and Binary Heap

A Tale of Two Trees: New Analysis for AVL Tree and Binary Heap

Algorithmic Building Blocks for Asymmetric Memories

Space Complexity Analysis of the Binary Tree Roll Algorithm

Contact Info

Product

Resources

About