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 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 New lower bounds on the cost of binary search trees

1996 ◽  
Vol 156 (1-2) ◽  
pp. 315-325 ◽  
Author(s):  
Roberte De Prisco ◽  
Alfredo De Santis
Keyword(s):  
Lower Bounds ◽  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees ◽  
The Cost

scholarly journals The stretch-length tradeoff in geometric networks: average case and worst case study

2015 ◽  
Vol 159 (1) ◽  
pp. 125-151
Author(s):  
DAVID ALDOUS ◽  
TAMAR LANDO
Keyword(s):  
Lower Bounds ◽  
Poisson Point Process ◽  
Euclidean Distance ◽  
Unit Area ◽  
Average Density ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Average Case ◽  
Route Length

AbstractConsider a network linking the points of a rate-1 Poisson point process on the plane. Write Ψave(s) for the minimum possible mean length per unit area of such a network, subject to the constraint that the route-length between every pair of points is at moststimes the Euclidean distance. We give upper and lower bounds on the function Ψave(s), and on the analogous “worst-case” function Ψworst(s) where the point configuration is arbitrary subject to average density one per unit area. Our bounds are numerically crude, but raise the question of whether there is an exponent α such that each function has Ψ(s) ≍ (s− 1)−αass↓ 1.

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
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