7 research outputs found
Gap terminology and related combinatorial properties for AVL trees and Fibonacci-isomorphic trees
We introduce gaps that are edges or external pointers in AVL trees such that the height difference between the subtrees rooted at their two endpoints is equal to 2. Using gaps we prove the Basic-Theorem that illustrates how the size of an AVL tree (and its subtrees) can be represented by a series of powers of 2 of the heights of the gaps, this theorem is the first such simple formula to characterize the number of nodes in an AVL tree. Then, we study the extreme case of AVL trees, the perfectly unbalanced AVL trees, by introducing Fibonacci-isomorphic trees that are isomorphic to Fibonacci trees of the same height and showing that they have the maximum number of gaps in AVL trees. Note that two ordered trees (such as AVL trees) are isomorphic iff there exists a one-to-one correspondence between their nodes that preserves not only adjacency relations in the trees, but also the roots. In the rest of the paper, we study combinatorial properties of Fibonacci-isomorphic trees. (C) 2018 Kalasalingam University. Publishing Services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/)
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
MSO Queries on Trees: Enumerating Answers under Updates Using Forest Algebras
We describe a framework for maintaining forest algebra representations that
are of logarithmic height for unranked trees. Such a representations can be
computed in O(n) time and updated in O(log(n)) time. The framework is of
potential interest for data structures and algorithms for trees whose
complexity depend on the depth of the tree (representation). We provide an
exemplary application of the framework to the problem of efficiently
enumerating answers to MSO-definable queries over trees which are subject to
local updates. We exhibit an algorithm that uses an O(n) preprocessing phase
and enumerates answers with O(log(n)) delay between them. When the tree is
updated, the algorithm can avoid repeating expensive preprocessing and restart
the enumeration phase within O(log(n)) time. Our algorithms and complexity
results in the paper are presented in terms of node-selecting tree automata
representing the MSO queries
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