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(Un)expected path lengths of asymmetric binary search trees
[chapter]

1993
*
Lecture Notes in Computer Science
*

*The*traditional

*model*

*of*

*binary*search

*trees*(

*BST*)

*of*size 2r + 1, r E /No, is characterized by

*the*family ~2(2r + 1), in which

*the*

*probability*prob(T)

*of*a

*tree*T E ~'~(2r + 1) is recursively defined ... We systematically deform

*the*

*probability*

*model*

*of*

*binary*search

*trees*using three different kinds

*of*deformers which are controlled by a real constant c and, using singularity

*analysis*, we obtain

*the*surprising ... For t = 2,

*the*BPM coincides with

*the*

*BST*-

*model*. t:] A full

*average*

*case*

*analysis*

*of*additive weights

*of*unlabelled rooteci planar t-ary

*trees*with polynomial weight functions

*under*

*the*BPM is presented ...

##
###
Average-case analysis on simple families of trees using a balanced probability model

1993
*
Theoretical Computer Science
*

Martinez,

doi:10.1016/0304-3975(93)90306-e
fatcat:hxnaw6rikfa7rgobv66dsx4rry
*Average*-*case**analysis*on simple families*of**trees*using a balanced*probability**model*, Theoretical Computer Science 117 (1993) 99-112. ... We extend*the**binary*search*tree**model**of**probability*to simply generated families*of**trees*. In*the*resulting statistics, well-balanced*trees*are more likely than linear*trees*. ... Sections 3 and 4 show*the*kind*of*problems that arise in*the**average*-*case**analysis**of*statistics*under**the*balanced*model*.*The*first*case*covers*the**analysis**of*occupancy*under**the*balanced*model*. ...##
###
Patterns in random binary search trees

1997
*
Random structures & algorithms (Print)
*

In a randomly grown

doi:10.1002/(sici)1098-2418(199710)11:3<223::aid-rsa2>3.0.co;2-2
fatcat:csgqb42ei5b7tbxvacio56gatq
*binary*search*tree**BST**of*size n, any fixed pattern occurs with a frequency that is on*average*proportional to n. ... Deviations from*the**average**case*are highly unlikely and well quantified by a Gaussian law. ... ACKNOWLEDGMENT*The*authors are grateful to*the*referees for sympathetic remarks and useful suggestions. ...##
###
Emerging behavior as binary search trees are symmetrically updated

2003
*
Theoretical Computer Science
*

When repeated updates are made to a

doi:10.1016/s0304-3975(02)00651-5
fatcat:bqf267yqkjbhjdchibzu4myvh4
*binary*search*tree*,*the*expected search cost tends to improve, as observed by Knott. ...*The*contribution*of*this paper is to*model*separately several di erent trends which may contribute to or detract from*the*Knott e ect, including a previously unreported centripetal tendency. ...*binary*search*trees**under*update. ...##
###
Reductions in binary search trees

2006
*
Theoretical Computer Science
*

We analyze two bottom-up reduction algorithms over

doi:10.1016/j.tcs.2005.12.015
fatcat:ts56copjezf6ngw4sqjylfugiy
*binary**trees*that represent replaceable data within a certain system, assuming*the**binary*search*tree*(*BST*) probabilistic*model*. ... In both*cases*,*the**average*size*of**the*reduced*tree*, as well as*the*cost to obtain it, is asymptotically linear with respect to*the*size*of**the*original*tree*. ... In particular, we are grateful to one*of*them who found a mistake in*the*computation*of**the*constants related to*the*variance*of**the*size*of**the*reduced*trees*. ...##
###
OBST: A Self-Adjusting Peer-to-Peer Overlay Based on Multiple BSTs
[article]

2013
*
arXiv
*
pre-print

We propose a simple overlay topology Obst(k) which is composed

arXiv:1309.3319v1
fatcat:tw35pqdc4vb37mkuhzfsqcfv3y
*of*k (rooted and directed)*Binary*Search*Trees*(*BSTs*), where k is a parameter. ... Today,*the*corresponding optimization tradeoffs are fairly well-understood, at least in*the*static*case*and from a worst-*case*perspective. ... Ross [25] for providing us with*the*BitTorrent data. ...##
###
OBST: A self-adjusting peer-to-peer overlay based on multiple BSTs

2013
*
IEEE P2P 2013 Proceedings
*

We propose a simple overlay topology OBST(k) which is composed

doi:10.1109/p2p.2013.6688721
dblp:conf/p2p/AvinBS13
fatcat:xzswecvcevaabmy7d5fbs4dsri
*of*k (rooted and directed)*Binary*Search*Trees*(*BSTs*), where k is a parameter. ... Today,*the*corresponding optimization tradeoffs are fairly well-understood, at least in*the*static*case*and from a worst-*case*perspective. ... Ross [25] for providing us with*the*BitTorrent data. ...##
###
The Ubiquitous Digital Tree
[chapter]

2006
*
Lecture Notes in Computer Science
*

*Under*various guises, it has then surfaced in

*the*management

*of*very large data bases, in

*the*design

*of*efficient communication protocols, in quantitative data mining, in

*the*leader election problem

*of*...

*The*algorithms are invariably very simple, easy to implement, and in a number

*of*

*cases*surprisingly efficient. ... Like for many probabilistic algorithms, what is in fact relevant is

*the*"typical" behaviour

*of*

*the*trie, measured either on

*average*or in

*probability*

*under*realistic data

*models*. ...

##
###
Efficient reorganization of binary search trees
[chapter]

1994
*
Lecture Notes in Computer Science
*

*The*

*average*access cost to

*the*

*tree*

*under*this rule is shown to

*equal*

*the*value achieved by

*the*common rule Move to

*the*Root (MTR). ... We consider

*the*problem

*of*maintaining a

*binary*search

*tree*that minimizes

*the*

*average*access cost needed to satisfy randomly generated requests. ... Preliminaries Let denote

*the*

*average*access cost to a

*BST*

*of*elements, with

*the*access

*probabilities*1 , then, with

*the*root at level 0,

*Under*

*the*IRM, for any set

*of*keys with a given RPV, there exists ...

##
###
Data Structures and Advanced Models of Computation on Big Data (Dagstuhl Seminar 16101)

2016
*
Dagstuhl Reports
*

This report documents

doi:10.4230/dagrep.6.3.1
dblp:journals/dagstuhl-reports/Lopez-OrtizMNS16
fatcat:svuxbjb4hrazzndruvxcbrjjuy
*the*program and*the*outcomes*of*Dagstuhl Seminar 16101 "Data Structures and Advanced*Models**of*Computation on Big Data". ...*The*seminar covered both recent advances in*the*"classical" data structuring topics as well as new*models**of*computation adapted to modern architectures, scientific studies that reveal*the*need for such ...*The*bound depends only on*the**probability**of**the*most*probable*symbol, but a precise computation*of**the*expected value is still challenging. Participants ...##
###
Compaction for two models of logarithmic-depth trees: Analysis and Experiments
[article]

2021
*
arXiv
*
pre-print

We are interested in

arXiv:2005.12997v3
fatcat:ggkm6rj22fcqzmrrz4dm6cykra
*the*quantitative*analysis**of**the*compaction ratio for two classical families*of**trees*: recursive*trees*and plane*binary*increasing*trees*. ... Finally, an experimental study is presented, based on a prototype implementation*of*compacted*binary*search*trees*that are*modeled*by plane*binary*increasing*trees*. ... In particular, we express our gratitude to one*of**the*referees who pointed out a subtle error and several smaller ones. All these persistent remarks have greatly increased*the*quality*of**the*paper. ...##
###
Efficient Reorganization of Binary Search Trees

2001
*
Algorithmica
*

We consider

doi:10.1007/s00453-001-0057-z
fatcat:4yg5iohklzdp5gqq7ql3avhwbq
*the*problem*of*maintaining a*binary*search*tree*(*BST*) that minimizes*the**average*access cost needed to satisfy randomly generated requests. ...*The**average*access cost to*the**tree**under*this rule is shown to*equal**the*value achieved by*the*common rule Move to*the*Root (MTR). ... Two anonymous referees have read*the*manuscript carefully, uncovered errors, drew our attention to references [6] - [9] , and contributed significantly to*the*accuracy and*the*clarity*of**the*presentation ...##
###
SplayNet: Towards Locally Self-Adjusting Networks

2016
*
IEEE/ACM Transactions on Networking
*

As a first step, we study distributed

doi:10.1109/tnet.2015.2410313
fatcat:egyatb7adbc63ppnxydt3tri3e
*binary*search*trees*(*BSTs*), which are attractive for their support*of*greedy routing. ... We introduce a simple*model*which captures*the*fundamental tradeoff between*the*benefits and costs*of*self-adjusting networks. ... Given an interval cut , we will denote*the*weighted empirical entropy*of*as: We can lower bound*the**average*communication cost*of*an (optimal)*binary*search*tree*as follows. ...##
###
The cost of offline binary search tree algorithms and the complexity of the request sequence

2008
*
Theoretical Computer Science
*

Third,

doi:10.1016/j.tcs.2007.12.015
fatcat:27dk2gehqfce3hzvefpowmtpyq
*the*expected cost*of*splay*trees*is within a constant factor*of**the*expected cost*of*an optimal offline*binary*search*tree*algorithm in a subset*of*Markov chains. ... First, any offline*binary*search*tree*algorithm can be at most a constant factor away from*the*entropy*of**the*process producing*the*request sequence. ... Acknowledgment This work has been in part supported by*the*Academy*of*Finland. ...##
###
Merged Search Algorithms for Radio Frequency Identification Anticollision

2012
*
Mathematical Problems in Engineering
*

A splitting algorithm which is called

doi:10.1155/2012/609035
fatcat:nt4yuu3pnvhn5aw4zo7lsvgyeu
*Binary*Search*Tree*(*BST*) is well known for multitags arbitration. ... Performance*of**the*proposed algorithm is compared with*the*original*BST*according to time and power consumed during*the*arbitration process. ... Acknowledgments*The*authors are appreciative*of**the*financial support in*the*form*of*research grants from*the*National Science Council, Republic*of*China*under*Grant nos. ...
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