Understanding B-Tree Structures and Concepts

Aug 11, 2024

B-Tree Introduction

Overview

  • Dynamic multilevel index structure.
  • Used for organizing data in secondary memory.
  • Links to previous explanations of multilevel indexing and different types of indexes in the description box.

Key Concepts

Index Types

  • Primary Index: Directly maps to records.
  • Clustered Index: Data is physically organized according to the index.
  • Secondary Index: Additional indexes that reference primary keys.
  • Dense Index: Contains an entry for every key in the data record.
  • Sparse Index: Contains an entry for only some of the keys.

Key Value and Pointer

  • Key Value: The unique identifier for searching (e.g., roll number).
  • Pointer: Reference to the actual data location in secondary memory.
  • Example: In a book, the key value is the topic name, and the pointer is the page number.

Multilevel Indexing

  • In larger datasets, multiple levels of indexes may be created.
  • Inserting or deleting records requires updates in all relevant indexes, complicating management.

B-Tree Structure

Tree Basics

  • Nodes and Edges: Nodes are connected by edges; no cycles exist (unlike graphs).
  • Types of Nodes:
    • Root Node: The top node of the tree.
    • Intermediate Nodes: Nodes between root and leaves.
    • Leaf Nodes: The bottom nodes with no children.

Balanced Tree

  • A B-tree is a balanced tree, where all leaf nodes are at the same level.
  • Unbalanced trees have leaf nodes at different levels.

Nomenclature in B-Tree

Pointers

  • Block Pointer: Used to reference child nodes.
  • Record Pointer: Points to actual data in secondary memory.

Keys

  • Multiple keys can be stored in a single node.
  • Each key corresponds to a record pointer, which points to detailed data.

Order of B-Tree

  • Order (P): Maximum number of children a node can have.
  • Node Requirements:
    • Root Node: Can have P children.
    • Intermediate/Leaf Nodes: Can have between ⌈P/2⌉ and P children.

Example of Order 4 B-Tree

  • Maximum Children: 4 (for root and intermediate nodes).
  • Maximum Keys: P-1 (3 for order 4).
  • Record Pointers: Equal to keys (also 3).

Insertion and Search

  • Insert keys in sorted order to maintain binary search properties.
  • Record pointers refer to data in secondary memory based on key values.

Conclusion

  • B-trees are effective for multilevel indexing, balancing the need for organized access to large datasets while enabling efficient searches and updates.