Questions tagged [b-tree]
28 questions
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Are degree and order the same thing when referring to a B-Tree?
I know the term order of a B-tree. Recently I heard a new term: B tree with minimum degree of 2.
We know that the degree is related to a node but what is the degree of a tree?
Does degree impose any kind of a restriction on the height of a B-tree?
Debabratta Jena
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4
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What does it mean that B-tree leaves carry no information?
According to Wikipedia B-tree page, Knuth's definition fifth property is "All leaves appear in the same level and carry no information.".
What does it mean that they carry no information?
Does that mean that there are no more pointers to children…
Nimrod Yonatan Ben-Nes
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4
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1 answer
Max no. of keys of B-Tree of height h
I am reading about B-Tree through CLRS. One of the exercise problem is to express maximum number of keys in a BTree of height $h$ and minimum degree $t$.
Properties of BTree of $t$:
$t\ge 2$
Min. no of keys in a node is $t-1$ and max. number of…
Sab
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3
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2 answers
How do XFast and Y Fast Tries compare to B trees in performance?
I learned that Y fast tries support amortized loglog(u) time insertions , deletions. and loglog(u) time membership, successor and predecessor operations with O(n) space. So when n is closer to U in dense big data environments Y fast tries seem…
thambi
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2
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0 answers
Questions about the Dancing Tree data structure
I would be very grateful if someone can clarify a little bit about the Dancing tree data structure that the Reiser4 filesystem uses. It's a presentation topic that I picked, however, there seems to be little resource about it. The only things that I…
Huy Đỗ Nguyễn An
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2
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1 answer
How B Tree guarantees self balancing property?
Let's say we have a b tree of order 4 and it has 3 levels. All nodes are completely filled. Now if we want to insert a key with maximum value ( than all keys present in the tree). For this, we have to go to the rightmost node at the last level. As…
Brijesh joshi
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2
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1 answer
Why does CLRS refer to the disk parts as pages rather than blocks?
I recently decided to review the B-tree chapter (chapter 18, p 486 in 3ed) in Introduction Algorithms, and found that they call pages what I always referred to as blocks or clusters:
In order to amortize the time spent waiting for mechanical…
2xMax
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2
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2 answers
How to delete an element from a B-tree
There is a lot of information online on this specific topic, but I still don't quite understand how to delete elements from a B-tree.
For example, given the following tree, how would we delete 26 and 63?
Is there a general approach?
gamma
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1
vote
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Maximum node splits in B-tree in terms of insertions and branching order
Is there any algorithm to calculate maximum number of node splits that can occur in given number of insertions and highest branching order? Lets say I want to insert 10 elements to an empty B-tree with highest branching order of 3. Is there way to…
Amit Nachimovitz
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1
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1 answer
Deletion of record from B+ tree
I was going through the B+ tree deletion operation from the book Database System Concepts, 6th Edition by Henry F. Korth. One particular thing caught my attention.
A B+ tree is given. We have to delete the record "Gold" from this tree.
So we first…
Robur_131
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How many node does the final B-tree have?
I'm currently studying the B-Trees chapter of Introduction to Algorithms. One of the question from the chapter is:
Suppose that we insert the keys $\{1,2,...,n\}$ into an empty B-tree with minimum degree 2. How many nodes does the final B-tree…
user83753
1
vote
1 answer
Understanding B tree key deletion step from CLRS algorithm
CLRS explains B tree key deletion as follows:
If the key $k$ is in node $x$ and $x$ is a leaf, delete the key $k$ from $x$.
If the key $k$ is in node $x$ and $x$ is an internal node, do the following:
a. If the child $y$ that precedes $k$ in node…
Mahesha999
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How was the equation for the minimum nodes in a B-Tree dervied in the paper "The Ubiquitous B-Tree" by Comer 1979?
In the paper by Comer (1979), he shows this equation for the minimum number of nodes in a B-Tree
$$
\sum_{l=0}^{h}{d^{l}=\frac{d^{h}-1}{2d-1}}
$$
I tried to get this result myself by using the geometric sum formula on the series, $2, 2d, 2d^2,2d^3,…
qwsdcvghyu89
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How to decide between pre-emptive split or non pre-emptive split and pre-emptive or non pre-emptive merge for a BTree?
I am trying to implement a BTree. As far as I understand the lower the height of the Tree the faster the search (This could be wrong, please correct me if it is).
Is pre-emptive split with non-pre-emptive merge the best or non-pre-emptive split with…
Pragmatic
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1
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What order B-tree is this?
I am studying B-trees and reading Introduction to Algorithms by Cormen et al.
Unfortunately, they have this diagram Figure 18.1 and they do not list the order of the tree.
I understand that for a B-tree of order $m$, the tree has 5…
Stan Shunpike
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