scholarly journals A q -Analogue of the Path Length of Binary Search Trees

Algorithmica ◽  
2001 ◽  
Vol 31 (3) ◽  
pp. 433-441 ◽  
Author(s):  
H. Prodinger
Keyword(s):  
Path Length ◽  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees

Path Length of Binary Search Trees

1972 ◽  
Vol 22 (2) ◽  
pp. 225-234 ◽  
Author(s):  
T. C. Hu ◽  
K. C. Tan
Keyword(s):  
Path Length ◽  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees

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.

scholarly journals An almost sure result for path lengths in binary search trees

2003 ◽  
Vol 35 (02) ◽  
pp. 363-376
Author(s):  
F. M. Dekking ◽  
L. E. Meester
Keyword(s):  
Path Length ◽  
Random Variable ◽  
Random Permutation ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Binary Search Trees ◽  
Search Trees ◽  
Total Path Length ◽  
Path Lengths

This paper studies path lengths in random binary search trees under the random permutation model. It is known that the total path length, when properly normalized, converges almost surely to a nondegenerate random variableZ. The limit distribution is commonly referred to as the ‘quicksort distribution’. For the class 𝒜mof finite binary trees with at mostmnodes we partition the external nodes of the binary search tree according to the largest tree that each external node belongs to. Thus, the external path length is divided into parts, each part associated with a tree in 𝒜m. We show that the vector of these path lengths, after normalization, converges almost surely to a constant vector timesZ.

scholarly journals An almost sure result for path lengths in binary search trees

2003 ◽  
Vol 35 (2) ◽  
pp. 363-376 ◽  
Author(s):  
F. M. Dekking ◽  
L. E. Meester
Keyword(s):  
Path Length ◽  
Random Variable ◽  
Random Permutation ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Binary Search Trees ◽  
Search Trees ◽  
Total Path Length ◽  
Path Lengths

This paper studies path lengths in random binary search trees under the random permutation model. It is known that the total path length, when properly normalized, converges almost surely to a nondegenerate random variable Z. The limit distribution is commonly referred to as the ‘quicksort distribution’. For the class 𝒜m of finite binary trees with at most m nodes we partition the external nodes of the binary search tree according to the largest tree that each external node belongs to. Thus, the external path length is divided into parts, each part associated with a tree in 𝒜m. We show that the vector of these path lengths, after normalization, converges almost surely to a constant vector times Z.

scholarly journals A NEW WEIGHT BALANCED BINARY SEARCH TREE

2000 ◽  
Vol 11 (03) ◽  
pp. 485-513 ◽  
Author(s):  
SEONGHUN CHO ◽  
SARTAJ SAHNI
Keyword(s):  
Path Length ◽  
Search Time ◽  
Search Tree ◽  
Binary Search ◽  
Experimental Results ◽  
Binary Search Tree ◽  
Binary Search Trees ◽  
Search Trees ◽  
New Class ◽  
Avl Trees

We develop a new class of weight balanced binary search trees called β-balanced binary search trees (β-BBSTs). β-BBSTs are designed to have reduced internal path length. As a result, they are expected to exhibit good search time characteristics. Individual search, insert, and delete operations in an n node β-BBST take O( log n) time for [Formula: see text]. Experimental results comparing the performance of β-BBSTs, WB(α) trees, AVL-trees, red/black trees, treaps, deterministic skip lists and skip lists are presented. Two simplified versions of, β-BBSTs are also developed.

scholarly journals The Wiener Index of Random Trees

2002 ◽  
Vol 11 (6) ◽  
pp. 587-597 ◽  
Author(s):  
RALPH NEININGER
Keyword(s):  
Path Length ◽  
Probabilistic Models ◽  
Wiener Index ◽  
Binary Search ◽  
Random Trees ◽  
Binary Search Trees ◽  
Search Trees ◽  
Limit Laws ◽  
Recursive Trees ◽  
Asymptotic Correlations

The Wiener index is analysed for random recursive trees and random binary search trees in uniform probabilistic models. We obtain expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed point equations. Covariances, asymptotic correlations, and bivariate limit laws for the Wiener index and the internal path length are given.

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