The document summarizes key aspects of B+ trees. It defines B+ trees as a technique for organizing indexed files where all keys are located in the leaves. It notes that search paths from the root to any key will have the same length. It then outlines features of B+ trees including how pages are structured, that keys are duplicated in interior pages, and how insertion and deletion of keys is handled by splitting pages or redistributing keys.

1. UNIVERSIDAD DE SANBUENAVENTURA
CALI
B+ TREE
CESAR ANDRES PALACIOS
INGENIERIA DE SISTEMAS

2. B+ TREE

3. B+ Tree
B+ trees is a technique for organizing files indexed. One
of this is that all keys are found in the leaves and
therefore any path from the root to any of the keys have the
same length.
B +-trees occupy a little more space than B-trees, and this
happens to be duplication in some keys.

4. Features
Formally defines a B+ tree in the following manner:
1. Each page, except the root, contains between d and 2d elements.
2. Each page, except the root, has between d and 2d + 1 +
1 descendants. M is used to express the number of items per page.
3. The following page has at least two offspring.
4. The leaf pages are all the same level.
5. All keys are in leaf pages.
6. The root keys and interior pages are used as indices.

5. Insertion
insertion-B + trees is similar to the process of integration in tree-
B. When a key is full (m = 2d). In this case, the affected site is
divided into two, distributing the key m+ 1 as follows:
"The key in d first page of the left and the remaining d +
1 keys on the right page."A copy of the
key environmental predecessor up to page.

6. Insertion (below)
It may be
that the predecessor overflow
page again, then you
must repeat the above
process. It is important to
note that the overflow is
not a leaf page does not
duplicate keys. The propagatio
n process can get to the root,
in which case the tree
height can be increased by
one.

7. B + Tree Clearing
Deleting a key is a b + tree is relatively easy, since the
keys to delete pages are in the leaves. In general must distinguish the
following cases:
CASE 1:
If removing a key, m is greater than or equal ad then ends the erase
operation. The key root or internal pages do not change by more
than be a copy of the deleted key in the leaves.
Remove : key 25
Page A

8. B+ Tree Clearing
CASE 2:
If removing a key, then m is less ad must be a redistribution of
keys, both the index and in the pages leaves.
Remove : key 27
Page C
Page A Page B

9. Webgraphy
1. http://www.virtual.unal.edu.co/cursos/ingenieri
a/2001412/capitulos/cap8/85.html
2. http://www.seanster.com/BplusTree/BplusTree.
html
3. http://es.wikipedia.org/wiki/%C3%81rbol-B%2B

10. THANK YOU FOR THE ATTENTION