B* Trees Definition

A B* Tree with order m is a tree with the following properties:

1. Every page has a maximum of m descendents

2. Every node, except for the root and the terminal nodes, has at least é(2m – 1)/3ù children

3. The root, unless the tree only has one node, has at least two children

4. All terminal nodes appear on the same level, i.e., are the same distance from the root

5. A nonterminal node with K children contains K – 1 records.

6. A leaf page contains at least ë(2m – 1)/3 û keys and no more than m – 1 keys

Buffering of Pages: Virtual B-Trees

· Read the root into memory and keep it there.

· Keep as many top levels of the tree in RAM as is possible.

· Create a page buffer to hold some number of B-tree pages. If a needed page is already in the buffer then don’t read it from disk.

· A virtual B-Tree is one contained partly in both RAM and disk storage.

LRU Replacement

· Accessing a page from disk that is not in a page buffer is called a page fault.

· Two causes of page faults are:

· We have never used the page

· It was once in the buffer but has since been replace with a new page

· We can’t do anything about the first cause

· The second cause can be minimized through buffer management.

· The question is: Which page should be replaced when room for a new page is needed?

· A Least Recently Used algorithm (LRU) doesn’t simply choose the oldest page for replacement but rather chooses the page whose most recent request is oldest.

· The assumption is made that we are more likely to need a page that we have used recently than we are to need a page that we have never used or one that we used some time ago. The term for this kind of assumption is temporal locality.

Variable-length Records and Keys

· If we have variable length records then we cannot hold to the principle that each page has the same number of keys per page capacity.

· Rather than use a maximum and minimum number of keys per page, we need to use a maximum and minimum number of bytes.

· W might want to change the key promotion (center of TOOBIG) policy to bias towards the shortest variable-length keys rather than longer keys. The idea is that we want to have pages with the largest numbers of descendents up high in the tree, rather than at the leaf level.