scholarly journals Splaying a search tree in preorder takes linear time

1990 ◽  
Vol 13 (1) ◽  
pp. 186-186
Author(s):  
R. Chaudhuri ◽  
H. Höft

In this paper we prove that if the nodes of an arbitraryn-node binary search treeTare splayed according to the preorder sequence ofTthen the total time isO(n). This is a special case of the splay tree traversal conjecture of Sleator and Tarjan [1].

1991 ◽  
Vol 14 (3) ◽  
pp. 545-551
Author(s):  
R. Chaudhuri ◽  
H. Höft

In this paper we prove that if the nodes of an arbitraryn-node binary search treeTare splayed in the preorder sequence ofTthen the total time isO(n). This is a special case of the splay tree traversal conjecture of Sleator and Tarjan.


2019 ◽  
Author(s):  
Abi Wibowo

Salah satu penerapan teori pohon yang paling berguna dan dipakai yaitu konsep binary search tree dimana konsep ini memberikan struktur data yang memudahkan operasi pencarian, penambahan, dan penghapusan terhadap data. Operasi tersebut lebih efisien dan jauh lebih baik pada konsep ini dibanding sequential search pada senarai berkait dalam waktu eksekusi / run-time.Dari konsep binary search tree ini dikembangkan lagi suatu struktur penyimpanan data yang merupakan modifikasi dari binary search tree tersebut yaitu AVL-Tree dan Splay Tree yang masing-masing mempunyai keunggulan pada kasus tertentu yang sekarang ini sering dijumpai.AVL-Tree merupakan modifikasi binary search tree yang tinggi setiap upapohon kiri dan upapohon kanan sama atau setidaknya selisih antara keduanya tidak lebih dari 1. Keunggulan dari AVL-Tree antara lain untuk mengoptimasi pencarian data terutama untuk kasus pohon yang condong ke kiri atau ke kanan sehingga pencarian akan jauh lebih mudah apabila pohon tersebut seimbang. Kasus pohon yang condong ke kiri atau kanan itu mungkin saja terjadi terutama apabila penambahan elemen dan penghapusan elemen dilakukan terus-menerus dan tidak dapat diketahui urutannya.Sedangkan Splay-Tree justru kebalikan dari AVL-Tree yang tidak mempermasalahkan kecondongan upapohonnya namun setiap kali data diakses maka simpul dari data yang diakses tersebut akan dinaikkan keatas mendekati akar pohon. Data yang sering diakses / aktif akan berada dekat pada akar pohon sehingga data tersebut mudah Dengan demikian dapat disimpulkan bahwa penerapan teori pohon sangatlah bermanfaat dalam kajian struktur data.


Cryptography ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 4
Author(s):  
Bayan Alabdullah ◽  
Natalia Beloff ◽  
Martin White

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.


2021 ◽  
Author(s):  
ZEGOUR Djamel Eddine

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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