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

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 A repertoire for additive functionals of uniformly distributed m-ary search trees

2005 ◽  
Vol DMTCS Proceedings vol. AD,... (Proceedings) ◽  
Author(s):  
james Allen fill ◽  
Nevin Kapur
Keyword(s):  
Generating Functions ◽  
Path Length ◽  
Singularity Analysis ◽  
Search Trees ◽  
Hadamard Products ◽  
Space Requirement ◽  
Additive Functionals ◽  
Total Path Length ◽  
International Audience ◽  
Number Of Leaves

International audience Using recent results on singularity analysis for Hadamard products of generating functions, we obtain the limiting distributions for additive functionals on $m$-ary search trees on $n$ keys with toll sequence $(i) n^α$ with $α ≥ 0 (α =0$ and $α =1$ correspond roughly to the space requirement and total path length, respectively); $(ii) ln \binom{n} {m-1}$, which corresponds to the so-called shape functional; and $(iii) $$1$$_{n=m-1}$, which corresponds to the number of leaves.

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