Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees

1977 ◽  
Vol 9 (1) ◽  
Author(s):  
D.T. Lee ◽  
C.K. Wong
Keyword(s):  
Case Analysis ◽  
Binary Search ◽  
Worst Case Analysis ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Partial Region

scholarly journals Comparing Leaf and Root Insertion

2010 ◽  
Vol 44 ◽  
Author(s):  
Jaco Geldenhuys ◽  
Brink Van der Merwe
Keyword(s):  
Standard Method ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Average Case ◽  
Tree Leaf ◽  
Leaf Insertion

We consider two ways of inserting a key into a binary search tree: leaf insertion which is the standard method, and root insertion which involves additional rotations. Although the respective cost of constructing leaf and root insertion binary search trees trees, in terms of comparisons, are the same in the average case, we show that in the worst case the construction of a root insertion binary search tree needs approximately 50% of the number of comparisons required by leaf insertion.

scholarly journals The -Version of Binary Search Trees: An Average Case Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Helmut Prodinger
Keyword(s):  
Path Length ◽  
Case Analysis ◽  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees ◽  
Average Case Analysis ◽  
Average Case ◽  
Successful Search ◽  
The Individual ◽  
Individual Trees

Following a suggestion of Cichoń and Macyna, binary search trees are generalized by keeping (classical) binary search trees and distributing incoming data at random to the individual trees. Costs for unsuccessful and successful search are analyzed, as well as the internal path length.

STRONGER QUICKHEAPS

2011 ◽  
Vol 22 (04) ◽  
pp. 945-969
Author(s):  
GONZALO NAVARRO ◽  
RODRIGO PAREDES ◽  
PATRICIO V. POBLETE ◽  
PETER SANDERS
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Binary Search ◽  
Priority Queues ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Tree Algorithms ◽  
Amortized Complexity ◽  
Time Bounds

The Quickheap (QH) is a recent data structure for implementing priority queues which has proved to be simple and efficient in practice. It has also been shown to offer logarithmic expected amortized complexity for all of its operations. Yet, this complexity holds only when keys inserted and deleted are uniformly distributed over the current set of keys. This assumption is in many cases difficult to verify, and does not hold in some important applications such as implementing some minimum spanning tree algorithms using priority queues. In this paper we introduce an elegant model called a Leftmost Skeleton Tree (LST) that reveals the connection between QHs and randomized binary search trees, and allows us to define Randomized QHs. We prove that these offer logarithmic expected amortized complexity for all operations regardless of the input distribution. We also use LSTs in connection to α-balanced trees to achieve a practical α-Balanced QH that offers worst-case amortized logarithmic time bounds for all the operations. Both variants are much more robust than the original QHs. We show experimentally that randomized QHs behave almost as efficiently as QHs on random inputs, and that they retain their good performance on inputs where that of QHs degrades.

DYNAMIC OPTIMAL BINARY SEARCH TREE

1990 ◽  
Vol 01 (04) ◽  
pp. 449-463 ◽  
Author(s):  
A. P. KORAH ◽  
M. R. KAIMAL
Keyword(s):  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Basic Operation ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Insertion And Deletion ◽  
Optimal Tree

In this paper we present a strategy to maintain a dynamic optimal binary search tree. The algorithms for insertion and deletion use swapping as the basic operation. Since in average situations the tree reorganization is limited to local changes, it can be favourably compared with the local balancing algorithms. The present algorithms dynamically maintain the optimal tree with an amortized time of O(log2 n), where n is the total number of nodes in the tree. In the worst case situations, the algorithms take only O(n) time. This is significant when they are compared to the algorithms producing static optimal binary search trees.

Binary Search Trees: Average and Worst Case Behavior (Extended Abstract)

1976 ◽  
pp. 301-313 ◽  
Author(s):  
Reiner Güttler ◽  
Kurt Mehlhorn ◽  
Wolfgang Schneider ◽  
Norbert Wernet
Keyword(s):  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Worst Case Behavior

scholarly journals Cuckoo Hashing

2001 ◽  
Vol 8 (32) ◽  
Author(s):  
Rasmus Pagh ◽  
Flemming Friche Rodler
Keyword(s):  
Lower Bounds ◽  
Binary Search ◽  
Upper And Lower Bounds ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Average Case ◽  
Cuckoo Hashing ◽  
Perfect Hashing ◽  
Theoretical Performance

We present a simple and efficient dictionary with worst case constant lookup time, equaling the theoretical performance of the classic dynamic perfect hashing scheme of Dietzfelbinger et al. (<em>Dynamic perfect hashing: Upper and lower bounds. SIAM J. Comput., 23(4):738-761, 1994</em>). The space usage is similar to that of binary search trees, i.e., three words per key on average. The practicality of the scheme is backed by extensive experiments and comparisons with known methods, showing it to be quite competitive also in the average case.

scholarly journals On the Diameter of Tree Associahedra

10.37236/7762 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Jean Cardinal ◽  
Stefan Langerman ◽  
Pablo Pérez-Lantero
Keyword(s):  
Computer Science ◽  
Search Tree ◽  
Binary Search ◽  
The Other ◽  
Discrete Mathematics ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Natural Notion ◽  
Minimum Number

We consider a natural notion of search trees on graphs, which we show is ubiquitous in various areas of discrete mathematics and computer science. Search trees on graphs can be modified by local operations called rotations, which generalize rotations in binary search trees. The rotation graph of search trees on a graph $G$ is the skeleton of a polytope called the graph associahedron of $G$.We consider the case where the graph $G$ is a tree. We construct a family of trees $G$ on $n$ vertices and pairs of search trees on $G$ such that the minimum number of rotations required to transform one search tree into the other is $\Omega (n\log n)$. This implies that the worst-case diameter of tree associahedra is $\Theta (n\log n)$, which answers a question from Thibault Manneville and Vincent Pilaud. The proof relies on a notion of projection of a search tree which may be of independent interest.

Hierarchical Programming for Worst-Case Analysis of Power Grids

2018 ◽  
Author(s):  
Hatim Djelassi ◽  
Stephane Fliscounakis ◽  
Alexander Mitsos ◽  
Patrick Panciatici
Keyword(s):  
Case Analysis ◽  
Power Grids ◽  
Worst Case Analysis ◽  
Worst Case
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