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B-slack Trees: Space Efficient B-Trees
[chapter]

2014
*
Lecture Notes in Computer Science
*

*B*-slack

*trees*, a subclass of

*B*-

*trees*that have substantially better worst-case space complexity, are introduced. They store n keys in height O(log

*b*n), where

*b*is the maximum node degree. ... Updates can be performed in O(log

*b*2 n) amortized time. A relaxed balance version, which is well suited for concurrent implementation, is also presented. ... Thus, a

*b*-overslack

*tree*is a relaxed

*B*-slack

*tree*, but not a

*B*-slack

*tree*. Consider a

*b*-overslack

*tree*T of height h that contains n keys. ...

*B**-

*trees*are based on ordered binary

*trees*and the admissible placement presented in [1] . ... We present in this paper an efficient, flexible, and effective data structure,

*B**-

*trees*, for non-slicing floorplans. ... Pei-Ning Guo for providing us with the O-

*tree*package and the benchmark circuits. Their work on the O-

*tree*paves the way to the development of the

*B**-

*tree*. ...

##
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B Trees
[chapter]

2004
*
Handbook of Data Structures and Applications
*

That is called the "branching factor" of a

doi:10.1201/9781420035179.ch15
fatcat:3tqrvv2rxfe4fhdsfvpb2tpkzm
*B*-*tree*. • Every n-node*B*-*tree*has height O(lg n), therefore,*B*-*trees*can be used to implement many dynamic-set operations in time O(lg n). •*B*-*trees*generalize ... Creating an empty*B*-*tree*• To build a*B*-*tree*T, we first use*B*-*TREE*-CREATE to create an empty root node and then call*B*-*TREE*-INSERT to add new keys. • Both of these procedures use an auxiliary procedure ... step 3a or 3b as necessary to guarantee that we descend to a node containing at least t keys.*b*. ...##
###
B-slack trees: Highly Space Efficient B-trees
[article]

2017
*
arXiv
*
pre-print

*B*-slack

*trees*, a subclass of

*B*-

*trees*that have substantially better worst-case space complexity, are introduced. They store $n$ keys in height $O(\log_b n)$, where $

*b*$ is the maximum node degree. ... Updates can be performed in $O(\log_{\frac

*b*2} n)$ amortized time. A relaxed balance version, which is well suited for concurrent implementation, is also presented. ...

*B*-slack

*trees*A

*B*-slack

*tree*is a variant of a

*B*-

*tree*. ...

##
###
Modularizing B+-trees: Three-Level B+-trees Work Fine

2013
*
Very Large Data Bases Conference
*

The best selection in this paper formed three-level

dblp:conf/vldb/SasakiA13
fatcat:alvq75372bd4nbsg73utysjpfa
*B*+-*trees*and achieved two-or threefold performance improvement over a typical implementation of a*B*+-*tree*. ... While utilizing these works, we modularize*B*+*trees*in memory especially for write-intensive workloads. ... Section 4.2 measures the baseline performance of our prototype of*B*+*trees*that are modularized and a typical implementation of a*B*+-*tree*, Google's C++*B*-*tree*[14]. ...##
###
Prefix B-trees

1977
*
ACM Transactions on Database Systems
*

Two modifications of

doi:10.1145/320521.320530
fatcat:rdrq7sqrojedlmlhpycml3pupm
*B*-*trees*are described, simple prefix*B*-*trees*and prefix*B*-*trees*. Both store only parts of keys, namely prefixes, in the index part of a*B**-*tree*. ... Prefix*B*-*trees*are designed to combine some of the advantages of*B*-*trees*, digital search*trees*, and key compression techniques while reducing the processing overhead of compression techniques. ... A simple prefix*B*-*tree*is a*B**-*tree*in which the*B**-index is replaced by a*B*-*tree*of (variable length) separators. Note. ...##
###
Ubiquitous B-Tree

1979
*
ACM Computing Surveys
*

It discusses the major variations of the

doi:10.1145/356770.356776
fatcat:t457kqnp75agjh3jyyjxgp6bn4
*B*-*tree*, especially the*B*+-*tree*, contrasting the relatwe merits and costs of each implementatmn. ...*B*-*trees*have become, de facto, a standard for file organization. ... THE BASIC*B*-*TREE*The*B*-*tree*has a short but important history. ...##
###
Belga B-Trees
[chapter]

2019
*
Lecture Notes in Computer Science
*

We prove lower bounds for the

doi:10.1007/978-3-030-19955-5_9
fatcat:gfy5gtqck5ak3jhl5aki3bkklq
*B*-*Tree*model, and introduce a*B*-*Tree*model data structure, the Belga*B*-*tree*, that executes any sequence of searches within a O(log log N ) factor of the best offline*B*-*tree*... Here we formalize the*B*-*Tree*model as a natural generalization of the BST model. ... We store each preferred path in a balanced classic*B*-*tree*. We call such classic*B*-*trees*auxiliary*trees*. Our dynamic*B*-*tree*will be a*tree*of classic*B*-*trees*. ...##
###
Belga B-trees
[article]

2019
*
arXiv
*
pre-print

We prove lower bounds for the

arXiv:1903.03560v1
fatcat:awekkj5mfjfwva4g3agy7wk2ve
*B*-*Tree*model, and introduce a*B*-*Tree*model data structure, the Belga*B*-*tree*, that executes any sequence of searches within a O( N) factor of the best offline*B*-*tree*model ... Here we formalize the*B*-*Tree*model as a natural generalization of the BST model. ... We store each preferred path in a balanced classic*B*-*tree*. We call such classic*B*-*trees*auxiliary*trees*. Our dynamic*B*-*tree*will be a*tree*of classic*B*-*trees*. ...##
###
Skip B-Trees
[chapter]

2006
*
Lecture Notes in Computer Science
*

We describe a new data structure, the Skip

doi:10.1007/11795490_28
fatcat:yoxjh4x3yfgzlnc4cmfxbxy7ly
*B*-*Tree*that combines the advantages of skip graphs with features of traditional*B*-*trees*. ... A skip*B*-*Tree*provides efficient search, insertion and deletion operations. ... In practice just as in*B*-*trees*, our cost is a very small constant (2-3) for reasonably large*b*(say, 10 7 ). ...##
###
STORAGE OVERHEAD OF O-TREES, B-TREES AND PREFIX B-TREES: A COMPARATIVE ANALYSIS

1996
*
International Journal of Foundations of Computer Science
*

The O-

doi:10.1142/s0129054196000166
fatcat:ouzd5klarndopjabjmsbbvcbyq
*tree*is an indexing mechanism closely related to*B*-*trees*and Pre x*B*-*trees*. ... In this paper we derive the expected storage overhead of O-*Trees*under the standard Bernoulli model of randomness, compare the results with the expected overhead of Btrees and Pre x*B*-*trees*under the same ... Two versions of Pre x*B*-*trees*are presented in 3]: Simple Pre x*B*-*trees*and Canonical Pre x*B*-*trees*. ...##
###
Write-Optimized B-Trees
[chapter]

2004
*
Proceedings 2004 VLDB Conference
*

of indirection for locating

doi:10.1016/b978-012088469-8.50060-7
dblp:conf/vldb/Graefe04
fatcat:2qg32qrzkneorlbshbpf4vfc7u
*B*-*tree*nodes on disk. ... The presented design enables large writes of internal*B*-*tree*nodes and leaves. ... Page migration in a*B*-*tree*with fence keys. ...##
###
Modern B-Tree Techniques

2010
*
Foundations and Trends in Databases
*

to

doi:10.1561/1900000028
fatcat:uisqivwiqre4jg2yug4vf6u3ve
*B*-*tree*indexes (Section 6), and*B*-*trees*with advanced key structures (Section 7). ... Perspectives on*B*-*trees*Complementing this "data structures perspective" on*B*-*trees*is the following "algorithms perspective." ...##
###
Edge-b-coloring Trees
[article]

2015
*
arXiv
*
pre-print

This problem was introduced by Irving and Manlove in 1999, where they showed that computing

arXiv:1511.05422v1
fatcat:6zfkqybl7jhdldlq7axh7y6kea
*b*(G) is NP-hard in general and polynomial-time solvable for*trees*. ... The*b*-chromatic number of G is the maximum integer*b*(G) for which G has a*b*-coloring with*b*(G) colors. ... Because the existence of a*b*-coloring with k colors forces the existence of k vertices of degree k − 1, we get: χ(G) ≤*b*(G) ≤ m(G) They then proved that*b*(G) ≥ m(G) − 1 whenever G is a*tree*. ...##
###
Persistently cached B-trees

2003
*
IEEE Transactions on Knowledge and Data Engineering
*

A notable feature of the approach is its compatibility with ordinary

doi:10.1109/tkde.2003.1198400
fatcat:jl54iy3ghvgrrnrahid75vgb7m
*B*-*trees*it exploits only the otherwise unused area of each*B*-*tree*page, and the basic behavior of*B*-*trees*need not be changed. ... This paper presents an approach to enhancing*B*-*tree*indexing performance by using a replication technique called persistent caching. ... When a*B*-*tree*is constructed by successively inserting random keys into a null*B*-*tree*, we s a y the*B*-*tree*is a random*B*-*tree*. ...
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