On Self-stabilizing Search Trees

2006 ◽  
pp. 76-89 ◽  
Author(s):  
Doina Bein ◽  
Ajoy K. Datta ◽  
Lawrence L. Larmore
Keyword(s):  
Search Trees

RCU‐HTM: A generic synchronization technique for highly efficient concurrent search trees

2021 ◽  
Author(s):  
Dimitrios Siakavaras ◽  
Konstantinos Nikas ◽  
Georgios Goumas ◽  
Nectarios Koziris
Keyword(s):  
Search Trees ◽  
Highly Efficient

Practical concurrent traversals in search trees

2018 ◽  
Vol 53 (1) ◽  
pp. 207-218
Author(s):  
Dana Drachsler-Cohen ◽  
Martin Vechev ◽  
Eran Yahav
Keyword(s):  
Search Trees

scholarly journals Extremal Values of the Sackin Tree Balance Index

2021 ◽  
Author(s):  
Mareike Fischer
Keyword(s):  
Phylogenetic Trees ◽  
Theoretical Computer Science ◽  
Search Trees ◽  
Formal Proofs ◽  
Birth Process ◽  
Ordered Trees ◽  
Research Areas ◽  
New Findings ◽  
Mathematical Phylogenetics ◽  
Extremal Values

AbstractTree balance plays an important role in different research areas like theoretical computer science and mathematical phylogenetics. For example, it has long been known that under the Yule model, a pure birth process, imbalanced trees are more likely than balanced ones. Also, concerning ordered search trees, more balanced ones allow for more efficient data structuring than imbalanced ones. Therefore, different methods to measure the balance of trees were introduced. The Sackin index is one of the most frequently used measures for this purpose. In many contexts, statements about the minimal and maximal values of this index have been discussed, but formal proofs have only been provided for some of them, and only in the context of ordered binary (search) trees, not for general rooted trees. Moreover, while the number of trees with maximal Sackin index as well as the number of trees with minimal Sackin index when the number of leaves is a power of 2 are relatively easy to understand, the number of trees with minimal Sackin index for all other numbers of leaves has been completely unknown. In this manuscript, we extend the findings on trees with minimal and maximal Sackin indices from the literature on ordered trees and subsequently use our results to provide formulas to explicitly calculate the numbers of such trees. We also extend previous studies by analyzing the case when the underlying trees need not be binary. Finally, we use our results to contribute both to the phylogenetic as well as the computer scientific literature using the new findings on Sackin minimal and maximal trees to derive formulas to calculate the number of both minimal and maximal phylogenetic trees as well as minimal and maximal ordered trees both in the binary and non-binary settings. All our results have been implemented in the Mathematica package SackinMinimizer, which has been made publicly available.

On the encipherment of search trees and random access files

1975 ◽  
Vol 10 (3) ◽  
pp. 10-10
Author(s):  
R. Bayer ◽  
J. K. Metzger ◽  
München W. Germany
Keyword(s):  
Random Access ◽  
Search Trees

Effect of portable fine-grained locality on energy efficiency and performance in concurrent search trees

2016 ◽  
Vol 51 (8) ◽  
pp. 1-2 ◽  
Author(s):  
Ibrahim Umar ◽  
Otto J. Anshus ◽  
Phuong H. Ha
Keyword(s):  
Energy Efficiency ◽  
Search Trees ◽  
Fine Grained ◽  
And Performance

An analytic approach for the analysis of rotations in fringe-balanced binary search trees

1998 ◽  
Vol 2 (2) ◽  
pp. 173-184 ◽  
Author(s):  
Alois Panholzer ◽  
Helmut Prodinger
Keyword(s):  
Binary Search ◽  
Analytic Approach ◽  
Binary Search Trees ◽  
Search Trees

Efficient algorithms for finding depth-first and breadth-first search trees in permutation graphs

1994 ◽  
Vol 49 (1) ◽  
pp. 45-50 ◽  
Author(s):  
C. Rhee ◽  
Y.Daniel Liang ◽  
S.K. Dhall ◽  
S. Lakshmivarahan
Keyword(s):  
Efficient Algorithms ◽  
Search Trees ◽  
Breadth First Search ◽  
Permutation Graphs

FINDING AN OPTIMAL BRIDGE BETWEEN TWO POLYGONS

2002 ◽  
Vol 12 (03) ◽  
pp. 249-261 ◽  
Author(s):  
XUEHOU TAN
Keyword(s):  
Hierarchical Structure ◽  
Shortest Path ◽  
Line Segment ◽  
Euclidean Distance ◽  
Geodesic Distance ◽  
Simple Polygon ◽  
Time Algorithm ◽  
Search Trees ◽  
Bridge Problem ◽  
Path Queries

Let π(a,b) denote the shortest path between two points a, b inside a simple polygon P, which totally lies in P. The geodesic distance between a and b in P is defined as the length of π(a,b), denoted by gd(a,b), in contrast with the Euclidean distance between a and b in the plane, denoted by d(a,b). Given two disjoint polygons P and Q in the plane, the bridge problem asks for a line segment (optimal bridge) that connects a point p on the boundary of P and a point q on the boundary of Q such that the sum of three distances gd(p′,p), d(p,q) and gd(q,q′), with any p′ ∈ P and any q′ ∈ Q, is minimized. We present an O(n log 3 n) time algorithm for finding an optimal bridge between two simple polygons. This significantly improves upon the previous O(n2) time bound. Our result is obtained by making substantial use of a hierarchical structure that consists of segment trees, range trees and persistent search trees, and a structure that supports dynamic ray shooting and shortest path queries as well.

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