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Chapter 14: Problem 5

What is the order \(p\) of a B-tree? Describe the structure of B-tree nodes.

Short Answer

Expert verified
The order \(p\) of a B-tree is the maximum number of children that a node can have, and each node can hold up to \(p-1\) keys. A B-tree node consists of keys and pointers to child nodes, which are organized in a way that ensures efficient search, insert, and delete operations. The root node has some unique characteristics compared to other nodes.

Step by step solution

01

Definition of Order

In B-trees, the order, denoted as \(p\), is a parameter that dictates the number of keys a node can hold, and the number of children that the node can have. The order of a B-tree is often defined as the maximum number of children for a node, which is usually set to ensure balance and optimize searching, insertion, and deletion operations. The minimum number of keys a non-root node can hold is usually \(\lceil p/2 \rceil -1\) keys.
02

Node Structure

A B-tree node contains keys and pointers. Each node can have a maximum of \(p-1\) keys and \(p\) children, where \(p\) is the order of the B-tree. For a non-root node with \(k\) keys, it has \(k+1\) child nodes. The keys act as separation values which divide its subtrees. For example, if a node contains the values [20, 40, 60] then the left child node contains values less than 20, the second child node contains values between 20 and 40, the third child node contains values between 40 and 60, and the right child node contains values greater than 60.
03

Root Node Description

The root node is the topmost node in a B-tree. Unlike other nodes, the root node can hold between 1 and \(p-1\) keys and have up to \(p\) children. If the tree is not empty, the root must have at least two children.

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Most popular questions from this chapter

How does multilevel indexing improve the efficiency of searching an index file?

as key field includes records with the following Part# values: 23,65,37,60,46,92,48, 71,56,59,18,21,10,74,78,15,16,20,24,28,39, 43,47,50,69,75,8,… # A PARTS file with Part# as key field includes records with the following Part# values: 23,65,37,60,46,92,48, 71,56,59,18,21,10,74,78,15,16,20,24,28,39, 43,47,50,69,75,8,49,33,38. Suppose that the search field values are inserted in the given order in a W -tree of order p = 4 and Pleaf = 3; show how the tree will expand and what the final tree will look like.

What is partitioned hashing? How does it work? What are its limitations?

What are the differences among primary, secondary, and clustering indexes? How do these differences affect the ways in which these indexes are implemented? Which of the indexes are dense, and which are not?

Why can we have at most one primary or clustering index on a file, but several secondary indexes?
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