scholarly journals An O(log log n)-Competitive Binary Search Tree with Optimal Worst-Case Access Times

2010 ◽  
pp. 38-49 ◽  
Author(s):  
Prosenjit Bose ◽  
Karim Douïeb ◽  
Vida Dujmović ◽  
Rolf Fagerberg
Keyword(s):  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Worst Case

scholarly journals Comparing Leaf and Root Insertion

2010 ◽  
Vol 44 ◽  
Author(s):  
Jaco Geldenhuys ◽  
Brink Van der Merwe
Keyword(s):  
Standard Method ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Average Case ◽  
Tree Leaf ◽  
Leaf Insertion

We consider two ways of inserting a key into a binary search tree: leaf insertion which is the standard method, and root insertion which involves additional rotations. Although the respective cost of constructing leaf and root insertion binary search trees trees, in terms of comparisons, are the same in the average case, we show that in the worst case the construction of a root insertion binary search tree needs approximately 50% of the number of comparisons required by leaf insertion.

DYNAMIC OPTIMAL BINARY SEARCH TREE

1990 ◽  
Vol 01 (04) ◽  
pp. 449-463 ◽  
Author(s):  
A. P. KORAH ◽  
M. R. KAIMAL
Keyword(s):  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Basic Operation ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Insertion And Deletion ◽  
Optimal Tree

In this paper we present a strategy to maintain a dynamic optimal binary search tree. The algorithms for insertion and deletion use swapping as the basic operation. Since in average situations the tree reorganization is limited to local changes, it can be favourably compared with the local balancing algorithms. The present algorithms dynamically maintain the optimal tree with an amortized time of O(log2 n), where n is the total number of nodes in the tree. In the worst case situations, the algorithms take only O(n) time. This is significant when they are compared to the algorithms producing static optimal binary search trees.

scholarly journals The Hidden Binary Search Tree

2018 ◽  
Author(s):  
Saulo Queiroz ◽  
Edimar Bauer
Keyword(s):  
Reference Values ◽  
Arbitrary Number ◽  
Input Sequence ◽  
Search Tree ◽  
Binary Search ◽  
Constant Time ◽  
Binary Search Tree ◽  
Worst Case ◽  
Balanced Tree

In this paper we review and enhance the Hidden Binary Search Tree (HBST) presented in [Queiroz 2017]. The HBST idea builds on the assumption an n-node self-balanced tree (e.g. AVL) requires to assure O(log2 n) worst-case search, namely, comparison between keys takes constant time. Therefore the size of each key in bits is fixed to B = O(log2 n) once n is determined, otherwise the O(1)-time comparison assumption does not hold. HBST generalizes the searchtree property such that the position of a node in the tree results from comparing its key against 'ideal' reference values associated to its ancestors. The first ideal values comes from the mid-point of the interval 0..2B. The strategy follows recursively such that the HBST height is bounded by O(B) regardless the input sequence of keys nor self-balancing procedures. In this paper we enhance the HBST to enable keys with arbitrary number of bits.

scholarly journals E-ART: A New Encryption Algorithm Based on the Reflection of Binary Search Tree

Cryptography ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 4
Author(s):  
Bayan Alabdullah ◽  
Natalia Beloff ◽  
Martin White
Keyword(s):  
Data Storage ◽  
Statistical Tests ◽  
Data Encryption ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Security Level ◽  
Avalanche Effect ◽  
High Security Level ◽  
Tree Data Structure

Data security has become crucial to most enterprise and government applications due to the increasing amount of data generated, collected, and analyzed. Many algorithms have been developed to secure data storage and transmission. However, most existing solutions require multi-round functions to prevent differential and linear attacks. This results in longer execution times and greater memory consumption, which are not suitable for large datasets or delay-sensitive systems. To address these issues, this work proposes a novel algorithm that uses, on one hand, the reflection property of a balanced binary search tree data structure to minimize the overhead, and on the other hand, a dynamic offset to achieve a high security level. The performance and security of the proposed algorithm were compared to Advanced Encryption Standard and Data Encryption Standard symmetric encryption algorithms. The proposed algorithm achieved the lowest running time with comparable memory usage and satisfied the avalanche effect criterion with 50.1%. Furthermore, the randomness of the dynamic offset passed a series of National Institute of Standards and Technology (NIST) statistical tests.

A graph build algorithm for layout compaction using binary search tree

2003 ◽  
Author(s):  
A. Arun ◽  
S.K. Saxena ◽  
D.R. Chowdhury
Keyword(s):  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree

Improving the Red-Black tree delete algorithm

2021 ◽  
Author(s):  
ZEGOUR Djamel Eddine
Keyword(s):  
Data Structure ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Search Performance ◽  
Running Time ◽  
Standard Algorithm ◽  
Color Changes ◽  
Red Black Tree ◽  
Symbol Tables

Abstract Today, Red-Black trees are becoming a popular data structure typically used to implement dictionaries, associative arrays, symbol tables within some compilers (C++, Java …) and many other systems. In this paper, we present an improvement of the delete algorithm of this kind of binary search tree. The proposed algorithm is very promising since it colors differently the tree while reducing color changes by a factor of about 29%. Moreover, the maintenance operations re-establishing Red-Black tree balance properties are reduced by a factor of about 11%. As a consequence, the proposed algorithm saves about 4% on running time when insert and delete operations are used together while conserving search performance of the standard algorithm.

O(log logn)-Competitive Binary Search Tree

2015 ◽  
pp. 1-4
Author(s):  
Chengwen Chris Wang ◽  
Daniel Sleator
Keyword(s):  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree
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