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B-Trees and B+ Trees. Brian Curless. Spring 2008. 2. Announcements (4/30/08). • Midterm on Friday. • Special office hour: 4:30-5:30 Thursday in Jaech. Gallery (6th floor of CSE building). – This is instead of my usual 11am office hour. • Reading for this lecture: Weiss Sec. 4.7. 3. Traversing very large datasets. Suppose we
B-Trees. Introduction. A B-tree is a specialized multiway tree designed especially for use on disk. In a B-tree each node may contain a large number of keys. The number of subtrees of each node, then, may also be large. A B-tree is designed to branch out in this large number of directions and to contain a lot of keys in each
8 Aug 2002 Similar to B trees, with a few slight differences. ? All data is stored at the leaf nodes (leaf pages); all other nodes (index pages) only store keys. ? Leaf pages are linked to each other. ? Keys may be duplicated; every key to the right of a particular key is >= to that key. Amir Kamil. 8/8/02. 2. B+ Tree Example.
DEF: A B-Tree of order m is an m-way tree such that. 1. All leaf nodes are at the same level. 2. All non-leaf nodes (except the root) have at most m and at least m/2 children. 3. The number of keys is one less than the number of children for non-leaf nodes and at most m-1 and at least m/2 for leaf nodes. 4. The root may have
B-trees are balanced search trees: height = O. ( log(n). ) for the worst case. • They were designed to work well on Direct Access secondary storage devices. (magnetic disks). • Similar to red-black trees, but show better performance on disk I/O opera- tions. • B-trees (and variants like B+ and B* trees ) are widely used in
EXERCISE 1. Construct a B+-tree for the following set of values. (2, 3, 5, 7, 11, 17, 19, 23, 29, 31). Assume that the tree is initially empty and values are inserted in ascending order. 1) Construct B+-trees for the cases where the number m of pointers that will fit a node is as follows: a. Four b. Seven. 2) Shows the form of the
1. University of Dublin. Trinity College. B+-Trees. Owen.Conlan@cs.tcd.ie. B+-Trees. 2. B+-Trees most common variant of B-tree index is B+- tree data pointers are stored only at the leaf nodes structure of leaf nodes differs from internal nodes leaf nodes have entry for every value of the search field along with a pointer to the
11 Jan 2005 four keys and five pointers represents the minimum size of a B Tree node. A B Tree contains only data pages. B Trees are dynamic. That is, the height of the tree grows and contracts as records are added and deleted. B+ Trees A B+ Tree combines features of ISAM and B Trees. It contains index pages and
Balanced Tree. • Same height for paths from root to leaf. • Given a search-key K, nearly same access time for different K values. – B+ Tree is constructed by parameter n. • Each Node (except root) has ?n/2? to n pointers. • Each Node (except root) has ?n/2?-1 to n-1 search-key values. B+ Tree Properties. P. 1. P. 2. P. 3. K.
At first, read the beginning of the chapter 18 from the text book. It explains why B-trees are used when the search structure is on disk. In this course, we consider B+-trees instead of classical B-trees introduced in the text book. The difference is that in B+-trees only leaf nodes contain the actual key values. The non- leaf nodes
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