scholarly journals Compressing Feature Sets with Digital Search Trees

2011 ◽  
Author(s):  
Vijay Chandrasekhar ◽  
Yuriy Reznik ◽  
Gabriel Takacs ◽  
David M. Chen ◽  
Sam S. Tsai ◽  
...  
Keyword(s):  
Search Trees ◽  
Feature Sets ◽  
Digital Search Trees ◽  
Digital Search

scholarly journals A weakly 1-stable distribution for the number of random records and cuttings in split trees

2011 ◽  
Vol 43 (01) ◽  
pp. 151-177 ◽  
Author(s):  
Cecilia Holmgren
Keyword(s):  
Classical Limit ◽  
Stable Distribution ◽  
Search Tree ◽  
Binary Search ◽  
Binary Search Tree ◽  
Search Trees ◽  
Infinitely Divisible ◽  
Digital Search Trees ◽  
Split Trees ◽  
Digital Search

In this paper we study the number of random records in an arbitrary split tree (or, equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for the convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of this number. After normalization the distributions are shown to be asymptotically weakly 1-stable. This work is a generalization of our earlier results for the random binary search tree in Holmgren (2010), which is one specific case of split trees. Other important examples of split trees includem-ary search trees, quad trees, medians of (2k+ 1)-trees, simplex trees, tries, and digital 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 Digital search trees and chaos game representation

2009 ◽  
Vol 13 ◽  
pp. 15-37 ◽  
Author(s):  
Peggy Cénac ◽  
Brigitte Chauvin ◽  
Stéphane Ginouillac ◽  
Nicolas Pouyanne
Keyword(s):  
Search Trees ◽  
Chaos Game Representation ◽  
Digital Search Trees ◽  
Chaos Game ◽  
Digital Search ◽  
Game Representation

scholarly journals Sorting strings and constructing digital search trees in parallel

1996 ◽  
Vol 154 (2) ◽  
pp. 225-245 ◽  
Author(s):  
Joseph F. JáJá ◽  
Kwan Woo Ryu ◽  
Uzi Vishkin
Keyword(s):  
Search Trees ◽  
Digital Search Trees ◽  
Digital Search

scholarly journals The expected profile of digital search trees

2011 ◽  
Vol 118 (7) ◽  
pp. 1939-1965 ◽  
Author(s):  
Michael Drmota ◽  
Wojciech Szpankowski
Keyword(s):  
Search Trees ◽  
Digital Search Trees ◽  
Digital Search

scholarly journals Digital search trees with m trees: Level polynomials and insertion costs

2011 ◽  
Vol Vol. 13 no. 3 (Analysis of Algorithms) ◽  
Author(s):  
Helmut Prodinger
Keyword(s):  
Analysis Of Algorithms ◽  
Approximate Counting ◽  
Search Trees ◽  
Digital Search Trees ◽  
International Audience ◽  
Digital Search

Analysis of Algorithms International audience We adapt a novel idea of Cichon's related to Approximate Counting to the present instance of Digital Search Trees, by using m (instead of one) such trees. We investigate the level polynomials, which have as coefficients the expected numbers of data on a given level, and the insertion costs. The level polynomials can be precisely described, thanks to formulae from q-analysis. The asymptotics of expectation and variance of the insertion cost are fairly standard these days and done with Rice's method.

scholarly journals Asymptotic variance of random symmetric digital search trees

2010 ◽  
Vol Vol. 12 no. 2 ◽  
Author(s):  
Hsien-Kuei Hwang ◽  
Michael Fuchs ◽  
Vytas Zacharovas
Keyword(s):  
Generating Functions ◽  
Asymptotic Variance ◽  
Shape Parameters ◽  
Search Trees ◽  
New Approach ◽  
Total Path Length ◽  
Digital Search Trees ◽  
Combined Use ◽  
International Audience ◽  
Digital Search

Dedicated to the 60th birthday of Philippe Flajolet International audience Asymptotics of the variances of many cost measures in random digital search trees are often notoriously messy and involved to obtain. A new approach is proposed to facilitate such an analysis for several shape parameters on random symmetric digital search trees. Our approach starts from a more careful normalization at the level of Poisson generating functions, which then provides an asymptotically equivalent approximation to the variance in question. Several new ingredients are also introduced such as a combined use of the Laplace and Mellin transforms and a simple, mechanical technique for justifying the analytic de-Poissonization procedures involved. The methodology we develop can be easily adapted to many other problems with an underlying binomial distribution. In particular, the less expected and somewhat surprising n (logn)(2)-variance for certain notions of total path-length is also clarified.

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