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

Uwe Trier
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  ... 
doi:10.1007/3-540-56610-4_99 fatcat:vjzte5rabvb7bbbxbhoyz2c7ka

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

R Casas, J Díaz, C Martínez
1993 Theoretical Computer Science  
Martinez, 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.  ... 
doi:10.1016/0304-3975(93)90306-e fatcat:hxnaw6rikfa7rgobv66dsx4rry

Patterns in random binary search trees

Philippe Flajolet, Xavier Gourdon, Conrado Mart�nez
1997 Random structures & algorithms (Print)  
In a randomly grown 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.  ... 
doi:10.1002/(sici)1098-2418(199710)11:3<223::aid-rsa2>3.0.co;2-2 fatcat:csgqb42ei5b7tbxvacio56gatq

Emerging behavior as binary search trees are symmetrically updated

Stephen Taylor, Marianne Durand
2003 Theoretical Computer Science  
When repeated updates are made to a 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.  ... 
doi:10.1016/s0304-3975(02)00651-5 fatcat:bqf267yqkjbhjdchibzu4myvh4

Reductions in binary search trees

José-Ramón Sánchez-Couso, María-Inés Fernández-Camacho
2006 Theoretical Computer Science  
We analyze two bottom-up reduction algorithms over 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.  ... 
doi:10.1016/j.tcs.2005.12.015 fatcat:ts56copjezf6ngw4sqjylfugiy

OBST: A Self-Adjusting Peer-to-Peer Overlay Based on Multiple BSTs [article]

Chen Avin, Michael Borokhovich, Stefan Schmid
2013 arXiv   pre-print
We propose a simple overlay topology Obst(k) which is composed 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.  ... 
arXiv:1309.3319v1 fatcat:tw35pqdc4vb37mkuhzfsqcfv3y

OBST: A self-adjusting peer-to-peer overlay based on multiple BSTs

Chen Avin, Michael Borokhovich, Stefan Schmid
2013 IEEE P2P 2013 Proceedings  
We propose a simple overlay topology OBST(k) which is composed 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.  ... 
doi:10.1109/p2p.2013.6688721 dblp:conf/p2p/AvinBS13 fatcat:xzswecvcevaabmy7d5fbs4dsri

The Ubiquitous Digital Tree [chapter]

Philippe Flajolet
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.  ... 
doi:10.1007/11672142_1 fatcat:aa7q6q4m45bi3gu5x5a35nyd6e

Efficient reorganization of binary search trees [chapter]

Micha Hofri, Hadas Shachnai
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  ... 
doi:10.1007/3-540-57811-0_13 fatcat:gqdaznwc4zfjhb3vmy3bly63lm

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

Alejandro Lopez-Ortiz, Ulrich Carsten Meyer, Markus E. Nebel, Robert Sedgewick, Marc Herbstritt
2016 Dagstuhl Reports  
This report documents 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  ... 
doi:10.4230/dagrep.6.3.1 dblp:journals/dagstuhl-reports/Lopez-OrtizMNS16 fatcat:svuxbjb4hrazzndruvxcbrjjuy

Compaction for two models of logarithmic-depth trees: Analysis and Experiments [article]

Olivier Bodini and Antoine Genitrini and Bernhard Gittenberger and Isabella Larcher and Mehdi Naima
2021 arXiv   pre-print
We are interested in 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.  ... 
arXiv:2005.12997v3 fatcat:ggkm6rj22fcqzmrrz4dm6cykra

Efficient Reorganization of Binary Search Trees

M. Hofri, H. Shachnai
2001 Algorithmica  
We consider 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  ... 
doi:10.1007/s00453-001-0057-z fatcat:4yg5iohklzdp5gqq7ql3avhwbq

SplayNet: Towards Locally Self-Adjusting Networks

Stefan Schmid, Chen Avin, Christian Scheideler, Michael Borokhovich, Bernhard Haeupler, Zvi Lotker
2016 IEEE/ACM Transactions on Networking  
As a first step, we study distributed 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.  ... 
doi:10.1109/tnet.2015.2410313 fatcat:egyatb7adbc63ppnxydt3tri3e

The cost of offline binary search tree algorithms and the complexity of the request sequence

Jussi Kujala, Tapio Elomaa
2008 Theoretical Computer Science  
Third, 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.  ... 
doi:10.1016/j.tcs.2007.12.015 fatcat:27dk2gehqfce3hzvefpowmtpyq

Merged Search Algorithms for Radio Frequency Identification Anticollision

Bih-Yaw Shih, Cheng-Wu Chen, Chen-Yuan Chen, Ta-Wei Lo
2012 Mathematical Problems in Engineering  
A splitting algorithm which is called 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.  ... 
doi:10.1155/2012/609035 fatcat:nt4yuu3pnvhn5aw4zo7lsvgyeu
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