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

Trevor Brown
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.  ... 
doi:10.1007/978-3-319-08404-6_11 fatcat:db5cjb2zt5es7p4orfo3syseju

B*-Trees

Yun-Chih Chang, Yao-Wen Chang, Guang-Ming Wu, Shu-Wei Wu
2000 Proceedings of the 37th conference on Design automation - DAC '00  
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.  ... 
doi:10.1145/337292.337541 dblp:conf/dac/ChangCWW00 fatcat:mh26j5jdmvgmtnzl7kxawcd5h4

B Trees [chapter]

Donghui Zhang
2004 Handbook of Data Structures and Applications  
That is called the "branching factor" of a 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.  ... 
doi:10.1201/9781420035179.ch15 fatcat:3tqrvv2rxfe4fhdsfvpb2tpkzm

B-slack trees: Highly Space Efficient B-trees [article]

Trevor Brown
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.  ... 
arXiv:1712.05020v2 fatcat:wlb5c6ktvjh6piyun6vfz36gvu

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

Shigero Sasaki, Takuya Araki
2013 Very Large Data Bases Conference  
The best selection in this paper formed three-level 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].  ... 
dblp:conf/vldb/SasakiA13 fatcat:alvq75372bd4nbsg73utysjpfa

Prefix B-trees

Rudolf Bayer, Karl Unterauer
1977 ACM Transactions on Database Systems  
Two modifications of 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.  ... 
doi:10.1145/320521.320530 fatcat:rdrq7sqrojedlmlhpycml3pupm

Ubiquitous B-Tree

Douglas Comer
1979 ACM Computing Surveys  
It discusses the major variations of the 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.  ... 
doi:10.1145/356770.356776 fatcat:t457kqnp75agjh3jyyjxgp6bn4

Belga B-Trees [chapter]

Erik D. Demaine, John Iacono, Grigorios Koumoutsos, Stefan Langerman
2019 Lecture Notes in Computer Science  
We prove lower bounds for the 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.  ... 
doi:10.1007/978-3-030-19955-5_9 fatcat:gfy5gtqck5ak3jhl5aki3bkklq

Belga B-trees [article]

Erik D.Demaine, John Iacono, Grigorios Koumoutsos, Stefan Langerman
2019 arXiv   pre-print
We prove lower bounds for the 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.  ... 
arXiv:1903.03560v1 fatcat:awekkj5mfjfwva4g3agy7wk2ve

Skip B-Trees [chapter]

Ittai Abraham, James Aspnes, Jian Yuan
2006 Lecture Notes in Computer Science  
We describe a new data structure, the Skip 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 ).  ... 
doi:10.1007/11795490_28 fatcat:yoxjh4x3yfgzlnc4cmfxbxy7ly

STORAGE OVERHEAD OF O-TREES, B-TREES AND PREFIX B-TREES: A COMPARATIVE ANALYSIS

RATKO ORLANDIC, HOSAM M. MAHMOUD
1996 International Journal of Foundations of Computer Science  
The O-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.  ... 
doi:10.1142/s0129054196000166 fatcat:ouzd5klarndopjabjmsbbvcbyq

Write-Optimized B-Trees [chapter]

Goetz Graefe
2004 Proceedings 2004 VLDB Conference  
of indirection for locating 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.  ... 
doi:10.1016/b978-012088469-8.50060-7 dblp:conf/vldb/Graefe04 fatcat:2qg32qrzkneorlbshbpf4vfc7u

Modern B-Tree Techniques

Goetz Graefe
2010 Foundations and Trends in Databases  
to 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."  ... 
doi:10.1561/1900000028 fatcat:uisqivwiqre4jg2yug4vf6u3ve

Edge-b-coloring Trees [article]

Victor Campos, Ana Silva
2015 arXiv   pre-print
This problem was introduced by Irving and Manlove in 1999, where they showed that computing 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.  ... 
arXiv:1511.05422v1 fatcat:6zfkqybl7jhdldlq7axh7y6kea

Persistently cached B-trees

K. Kato
2003 IEEE Transactions on Knowledge and Data Engineering  
A notable feature of the approach is its compatibility with ordinary 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.  ... 
doi:10.1109/tkde.2003.1198400 fatcat:jl54iy3ghvgrrnrahid75vgb7m
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