Another representation of binary tree traversal

1973 ◽  
Vol 2 (2) ◽  
pp. 52-54 ◽  
Author(s):  
Edward N. Adams
Keyword(s):  
Binary Tree ◽  
Tree Traversal

scholarly journals A Combinatorial Bijection on di-sk Trees

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Shishuo Fu ◽  
Zhicong Lin ◽  
Yaling Wang
Keyword(s):  
Binary Tree ◽  
Number Of Components ◽  
Symmetric Extension ◽  
Alternative Approach ◽  
Tree Traversal ◽  
Separable Permutations ◽  
Rooted Binary Tree ◽  
Schur Positive

A di-sk tree is a rooted binary tree whose nodes are labeled by $\oplus$ or $\ominus$, and no node has the same label as its right child. The di-sk trees are in natural bijection with separable permutations. We construct a combinatorial bijection on di-sk trees proving  the two quintuples $(\mathrm{LMAX},\mathrm{LMIN},\mathrm{DESB},\mathsf{iar},\mathsf{comp})$ and $(\mathrm{LMAX},\mathrm{LMIN},\mathrm{DESB},\mathsf{comp},\mathsf{iar})$ have the same distribution over separable permutations. Here for a permutation $\pi$, $\mathrm{LMAX}(\pi)/\mathrm{LMIN}(\pi)$ is the set of values of the left-to-right maxima/minima of $\pi$ and $\mathrm{DESB}(\pi)$ is the set of descent bottoms of $\pi$, while $\mathsf{comp}(\pi)$ and $\mathsf{iar}(\pi)$ are respectively  the number of components of $\pi$ and the length of initial ascending run of $\pi$.  Interestingly, our bijection specializes to a bijection on $312$-avoiding permutations, which provides  (up to the classical Knuth–Richards bijection) an alternative approach to a result of Rubey (2016) that asserts the  two triples $(\mathrm{LMAX},\mathsf{iar},\mathsf{comp})$ and $(\mathrm{LMAX},\mathsf{comp},\mathsf{iar})$ are equidistributed  on $321$-avoiding permutations. Rubey's result is a symmetric extension of an equidistribution due to Adin–Bagno–Roichman, which implies the class of $321$-avoiding permutations with a prescribed number of components is Schur positive.  Some equidistribution results for various statistics concerning tree traversal are presented in the end.

A Novel Encryption of Text Messages using Two Fold Approach

2019 ◽  
Vol 13 ◽  
Author(s):  
T. Sivakumar ◽  
S Veeramani ◽  
M Pandi ◽  
Ganesh Gopal
Keyword(s):  
Binary Tree ◽  
Secure Communication ◽  
Text Messages ◽  
Digital Data ◽  
Security Threats ◽  
New Methods ◽  
Xor Operation ◽  
Tree Traversal ◽  
Encryption Method ◽  
Tree Traversals

Background: The amount of digital data created and shared via internet has been increasing every day. The number of security threats has also increased due to the vulnerabilities present in the network hardware and software. Cryptography is the practice and study of techniques to secure communication in the presence of third parties. Though there are several cryptosystems to secure the information, there is a necessity to introduce new methods in order to protect information from the attackers. Objective: To propose a new encryption method using Binary Tree Traversal (BTT) and XOR operation to protect the text messages. Method: The proposed method uses both transposition and substitution techniques for converting plaintext into ciphertext. The notion binary tree traversal is adapted as transposition and bitwise XOR operation is used for substitution. Results: The repeating letters appeared in the plaintext are replaced with different cipher letters and placed on different location in the cipher text. Hence, it is infeasible to identify the plaintext message easily. The time taken by the proposed method for encryption is very less. Conclusion: A simple encryption method using binary tree traversals and XOR operation is developed. Encrypting data using binary tree traversals is a different way while compared with other traditional encryption methods. The proposed method is fast, secure and can be used to encrypt short messages in real time applications.

Dynamic Interpretation Method of XML Configuration Strategy for IP Mode Measurement and Control System

2010 ◽  
Vol 139-141 ◽  
pp. 2537-2541
Author(s):  
Xiao Bin Hong ◽  
Gui Xiong Liu ◽  
Jian Long Xu
Keyword(s):  
Control System ◽  
Binary Tree ◽  
Ethanol Concentration ◽  
Tree Model ◽  
Measurement And Control System ◽  
Dynamic Interpretation ◽  
Tree Traversal ◽  
And Control ◽  
Measurement And Control ◽  
Interpretation Method

The interoperability among diversified ubiquitous sensor network platforms can be solved well by employing XML technology. According to the requirement that implementing accurately remote XML configuration strategy for spot equipments, a new dynamic interpretation method of XML configuration strategy is proposed. First, an XML-based IP mode measurement & control system is introduced. On the basis of realizing graphical strategy editor, the innovative ways and technologies of some key problems for dynamic interpretation method were especially discussed in this paper, including configuration strategy conversion combining preorder binary tree traversal with stack, XML strategy decomposition based on DOM tree model and dynamical update of XML configuration strategy. Finally, an application example in IP mode ethanol concentration measurement & control system is introduced. Experimental results show that the new method can greatly simplify conversion from measurement & control strategy to microinstructions, which saves system resources and improves greatly the speed of interpretation.

A Novel Permutation Based Encryption Using Tree Traversal Approach.

2019 ◽  
Vol 13 ◽  
Author(s):  
T Sivakumar ◽  
S Veeramani ◽  
M Pandi ◽  
N Senthil Madasamy ◽  
Rakesh kumar
Keyword(s):  
Data Security ◽  
Binary Tree ◽  
Data Encryption ◽  
Digital Data ◽  
Digital Information ◽  
Internet Communication ◽  
Digital Form ◽  
Tree Traversal ◽  
Encryption And Decryption ◽  
Emerging Issues

: In 21st century one of the emerging issues is to secure the information stored and communicated in digital form. There is no assurance that the data we have sent may be hacked by any hacker and the data we have sent may reach correctly to the receiver or not. Thus, confidentiality, integrity, and authentication services play major role in Internet communication. Encryption is the process of encoding messages in such a way that only authorized parties can read and understand after successful decryption. Several data security techniques have been emerged in recent years, but still there is a need to develop new and different techniques to protect the digital information from attackers. This paper provides a new idea for data encryption and decryption using the notion of binary tree traversal to secure digital data. The proposed method is experimented and observed that the method is suitable for providing confidentiality service in real time.

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