Embedding complete ternary tree in hypercubes using AVL trees

A complete ternary tree is a tree in which every non-leaf vertex has exactly three children. We prove that a complete ternary tree of height h, TTh, is embeddable in a hypercube of dimension . This result coincides with the result of [2]. However, in this paper, the embedding utilizes the knowledge of AVL trees. We prove that a subclass of AVL trees is a subgraph of hypercube. The problem of embedding AVL trees in hypercube is an independent emerging problem

Data Structures for Indexing Triple Table

Import 03/11/2016Bakalářská práce je zaměřená na datové struktury využívané v sémantických databázích. Rešeršní část práce popisuje základní datové struktury, které se používají k indexování dat. Implementační část popisuje dvě datové struktury, a to konkrétně AVL-strom a Grid File, analyzuje jejich struktury i funkcionality a následně znázorňuje, jak vypadá jejich zavádění. Experimentální část testuje obě implementované datové struktury a porovnává je s ostatními strukturami tak, že provádí sadu definovaných příkazů a měří časy provedení dotazů. Závěrečná část práce analyzuje a srovnává naměřené časy pro všechny datové struktury a vyhodnocuje jejich výsledky.Bachelor thesis is focused on the data structures used in the semantic databases. The research part describes basic data structure that are used for data indexation. The implementation part describes two implemented data structures, AVL-tree and Grid File, analyses their structure and functionality and visualizes their implementation. The experimental part tests implemented data structures and compares them with the others by executing set of defined orders and by measuring time needed for requests accomplishment. The final part of the thesis analyses and compares measured times for all data structures and evaluates the results.460 - Katedra informatikydobř

Data structures

We discuss data structures and their methods of analysis. In particular, we treat the unweighted and weighted dictionary problem, self-organizing data structures, persistent data structures, the union-find-split problem, priority queues, the nearest common ancestor problem, the selection and merging problem, and dynamization techniques. The methods of analysis are worst, average and amortized case

Comparison of several sorting algorithms designed for nearly sorted lists

Quickersort, Straight Insertion Sort, Mehlhorn's AVL-tree Sorting Algorithm and Cook's new sorting algorithm are compared on nearly and nedium sorted lists. The ratio of the minimum number of list elements that must be removed so that the remaining portion of the list is in order to the size of the list is our measure. Tests on randomly generated lists of various combinations of list length and small and medium sortedness ratios indicate that Straight Insertion Sort is best for small or very nearly sorted lists, Cook's new sorting algorithm is best for nearly sorted lists and Quickersort is best otherwise. We also modify the AVL-tree Sorting Algorithm and it performs better than Quickersort on medium sorted lists

Efficient Data Structures and Algorithms for Scientific Computations.

Large-scale numerically intensive scientific applications can require tremendous amounts of computer time and space. Two general methods are presented for reducing the computer resources required in scientific computing. The first is a numerical database system which is built on a space and time optimal data structure called a weighted search tree and that allows for the storage and retrieval of valuable intermediate information so costly redundant calculations can be avoided. The second is a matrix algorithm based on a new space optimal representation of sparse matrices that for typical scientific applications can be expected to dramatically decrease the cost of multiplying sparse matrices. Codes and tests for each are given. Both methods can be implemented in a broad range of large-scale scientific applications

Search Tree Data Structures and Their Applications

This study concerns the discussion of search tree data structures and their applications. The thesis presents three new top-down updating algorithms for the concurrent data processing environment.Computing and Information Scienc

Data structures

We discuss data structures and their methods of analysis. In particular, we treat the unweighted and weighted dictionary problem, self-organizing data structures, persistent data structures, the union-find-split problem, priority queues, the nearest common ancestor problem, the selection and merging problem, and dynamization techniques. The methods of analysis are worst, average and amortized case

A parameterized model for selecting the optimum file organization in multi-attribute retrieval systems.

Massachusetts Institute of Technology, Alfred P. Sloan School of Management. Thesis. 1974. M.S.MICROFICHE COPY ALSO AVAILABLE IN DEWEY LIBRARY.Bibliography: leaves 135-142.M.S

Bulk updates and cache sensitivity in search trees

This thesis examines two topics related to binary search trees: cache-sensitive memory layouts and AVL-tree bulk-update operations. Bulk updates are also applied to adaptive sorting. Cache-sensitive data structures are tailored to the hardware caches in modern computers. The thesis presents a method for adding cache-sensitivity to binary search trees without changing the rebalancing strategy. Cache-sensitivity is maintained using worst-case constant-time operations executed when the tree changes. The thesis presents experiments performed on AVL trees and red-black trees, including a comparison with cache-sensitive B-trees. Next, the thesis examines bulk insertion and bulk deletion in AVL trees. Bulk insertion inserts several keys in one operation. The number of rotations used by AVL-tree bulk insertion is shown to be worst-case logarithmic in the number of inserted keys, if they go to the same location in the tree. Bulk deletion deletes an interval of keys. When amortized over a sequence of bulk deletions, each deletion requires a number of rotations that is logarithmic in the number of deleted keys. The search cost and total rebalancing complexity of inserting or deleting keys from several locations in the tree are also analyzed. Experiments show that the algorithms work efficiently with randomly generated input data. Adaptive sorting algorithms are efficient when the input is nearly sorted according to some measure of presortedness. The thesis presents an AVL-tree-based variation of the adaptive sorting algorithm known as local insertion sort. Bulk insertion is applied by extracting consecutive ascending or descending keys from the input to be sorted. A variant that does not require a special bulk-insertion algorithm is also given. Experiments show that applying bulk insertion considerably reduces the number of comparisons and time needed to sort nearly sorted sequences. The algorithms are also compared with various other adaptive and non-adaptive sorting algorithms