scholarly journals A hooray for Poisson approximation

2005 ◽  
Vol DMTCS Proceedings vol. AD,... (Proceedings) ◽  
Author(s):  
Rudolf Grübel
Keyword(s):  
Analysis Of Algorithms ◽  
Poisson Approximation ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Variation Distance ◽  
International Audience ◽  
Election Algorithm ◽  
Bernoulli Variables ◽  
Quantities Of Interest

International audience We give several examples for Poisson approximation of quantities of interest in the analysis of algorithms: the distribution of node depth in a binary search tree, the distribution of the number of losers in an election algorithm and the discounted profile of a binary search tree. A simple and well-known upper bound for the total variation distance between the distribution of a sum of independent Bernoulli variables and the Poisson distribution with the same mean turns out to be very useful in all three cases.

scholarly journals Random Records and Cuttings in Split Trees: Extended Abstract

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Cecilia Holmgren
Keyword(s):  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Search Trees ◽  
Digital Search Trees ◽  
International Audience ◽  
Split Trees ◽  
Digital Search

International audience We study the number of records in random split trees on $n$ randomly labelled vertices. Equivalently the number of random cuttings required to eliminate an arbitrary random split tree can be studied. After normalization the distributions are shown to be asymptotically $1$-stable. This work is a generalization of our earlier results for the random binary search tree which is one specific case of split trees. Other important examples of split trees include $m$-ary search trees, quadtrees, median of $(2k+1)$-trees, simplex trees, tries and digital search trees.

scholarly journals Almost sure asymptotics for the random binary search tree

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Matthew Roberts
Keyword(s):  
Random Permutation ◽  
Search Tree ◽  
Binary Search ◽  
Saturation Level ◽  
Binary Search Tree ◽  
International Audience ◽  
Permutation Model ◽  
Random Permutation Model

International audience We consider a (random permutation model) binary search tree with $n$ nodes and give asymptotics on the $\log$ $\log$ scale for the height $H_n$ and saturation level $h_n$ of the tree as $n \to \infty$, both almost surely and in probability. We then consider the number $F_n$ of particles at level $H_n$ at time $n$, and show that $F_n$ is unbounded almost surely.

scholarly journals Average depth in a binary search tree with repeated keys

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Margaret Archibald ◽  
Julien Clément
Keyword(s):  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Average Depth ◽  
Binary Search Trees ◽  
Search Trees ◽  
Random Sequences ◽  
International Audience ◽  
The Right

International audience Random sequences from alphabet $\{1, \ldots,r\}$ are examined where repeated letters are allowed. Binary search trees are formed from these, and the average left-going depth of the first $1$ is found. Next, the right-going depth of the first $r$ is examined, and finally a merge (or 'shuffle') operator is used to obtain the average depth of an arbitrary node, which can be expressed in terms of the left-going and right-going depths. The variance of each of these parameters is also found.

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.

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.

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