On the average internal path length of m-ary search trees

1986 ◽  
Vol 23 (1) ◽  
pp. 111-117 ◽  
Author(s):  
Hosam M. Mahmoud
Keyword(s):  
Path Length ◽  
Search Trees

scholarly journals Digital Search Trees Again Revisited: The Internal Path Length Perspective

1994 ◽  
Vol 23 (3) ◽  
pp. 598-616 ◽  
Author(s):  
Peter Kirschenhofer ◽  
Helmut Prodinger ◽  
Wojciech Szpankowski
Keyword(s):  
Path Length ◽  
Search Trees ◽  
Digital Search Trees ◽  
Digital Search

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.

ISA [k] trees: A class of binary search trees with minimal or near minimal internal path length

1993 ◽  
Vol 23 (11) ◽  
pp. 1267-1283
Author(s):  
Faris N. Abuali ◽  
Roger L. Wainwright
Keyword(s):  
Path Length ◽  
Binary Search ◽  
Binary Search Trees ◽  
Search Trees

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.

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