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Implementation and Analysis of B+ Trees

Overview

This project involves the implementation and analysis of B+ Trees, a widely-used data structure in computer science and database management systems. B+ Trees are optimized for database indexing, search, and retrieval operations. Our project explores the core concepts, design, and performance characteristics of B+ Trees, including insertion, deletion, search operations, and bulk loading techniques.

Project Team

  • Vismay Walde (2022MCB1283)
  • Shivam Zample (2022MCB1280)
  • Tejas Wagh (2022CSB1144)

Instructor: Dr. Anil Shukla
Teaching Assistant: E Harshith Kumar Yadav

Key Features

  • B+ Tree Implementation: Includes core operations like insertion, deletion, and search.
  • Performance Analysis: Evaluates time complexity and compares B+ Trees with B-Trees.
  • Bulk Loading: Demonstrates efficient bulk loading techniques for B+ Trees.

Structure

1. Introduction

B+ Trees are a balanced multi-way tree data structure used extensively in database systems to optimize search and retrieval operations. They address limitations of binary search trees and are essential for managing large datasets efficiently.

2. B+ Tree Structure

  • Internal Nodes: Serve as intermediaries with key-value pairs and pointers to child nodes.
  • Leaf Nodes: Contain actual data entries and are linked to facilitate ordered access.

3. Observations

  • Bulk Loading: Efficiently builds B+ Trees by sorting and inserting records in bulk, reducing I/O operations compared to repeated insertions.
  • Complexities: Search, insertion, and deletion operations have O(log n) complexity on average.

4. Algorithms

  • Search: Finds the leaf node containing the desired key.
  • Insertion: Adds a new entry, handling node splits and root adjustments as needed.
  • Deletion: Removes an entry, ensuring the tree remains balanced through redistributions or merges.

5. Conclusions

  • Advantages: B+ Trees offer efficient operations and are preferable to other balanced data structures.
  • Future Work: Includes dynamic B+ Trees, data compression techniques, and hybrid indexing systems.

6. Applications

  • Database Management Systems: Used for efficient data indexing.
  • Distributed File Systems: Maintains metadata across clusters.

Getting Started

  1. Clone the repository:

    git clone https://github.com/yourusername/bplus-tree-project.git

  2. Navigate to the project directory:

    cd bplus-tree-project

  3. Compile and run the project:

Acknowledgements

Special thanks to our instructor, Dr. Anil Shukla, and our Teaching Assistant, E Harshith Kumar Yadav, for their guidance and support throughout the project.

References