extendible hashing

Guri Bee

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19-10-2024

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Extendible Hashing: A Scalable Solution for Efficient Data Retrieval

Extendible hashing is a dynamic hashing technique designed to handle growing datasets while maintaining efficient data retrieval. It offers a balance between the simplicity of direct addressing and the flexibility of hash tables, making it a popular choice for database management systems and other applications requiring fast lookups.

Understanding the Basics

At its core, extendible hashing relies on a directory and a set of buckets.

• Directory: This is a table that maps hash values to bucket addresses. The size of the directory is a power of two, denoted by 2^d where d is the global depth.
• Buckets: These store the actual data records. Each bucket can hold a limited number of records, and when full, it gets split.

How Extendible Hashing Works

1. Hashing: When inserting a new record, its key is hashed using a hash function, producing a hash value.
2. Directory Lookup: The directory uses the d most significant bits of the hash value to find the corresponding bucket address.
3. Bucket Insertion: The record is inserted into the identified bucket.
4. Overflow Handling: If the bucket becomes full, it's split into two new buckets. This split also triggers a directory update:
   • Local Depth: Each new bucket gets assigned a local depth of d+1, meaning it uses one extra bit from the hash value for addressing.
   • Directory Doubling: If the local depth of any bucket exceeds the global depth, the directory is doubled in size, increasing d by 1. This ensures that all buckets are still addressable by the directory.

Advantages of Extendible Hashing

• Scalability: The directory and buckets grow dynamically as the dataset expands, eliminating the need for pre-allocation of space.
• Efficient Retrieval: Lookups are fast since the directory provides direct access to the correct bucket.
• Load Balancing: Data is distributed evenly across buckets, reducing the likelihood of collisions and improving performance.

Example: Managing a Library Catalog

Imagine a library using extendible hashing to store information about its books. Each book has a unique ISBN (International Standard Book Number) which serves as the key for hashing.

1. Initially, the directory has a global depth of d=1 (2 entries) and a single bucket with a local depth of 1.
2. As new books are added, the bucket might fill up.
3. When a bucket overflows, it's split, creating two buckets with a local depth of 2.
4. The directory is doubled if the local depth of any bucket exceeds the global depth, expanding its size to accommodate the new bucket addresses.

Extendible Hashing vs. Other Techniques

While extendible hashing offers advantages in scalability and performance, it's important to consider its limitations:

• Space Overhead: The directory can become large for extensive datasets, potentially consuming significant memory.
• Complexity: Implementing extendible hashing requires a deeper understanding of its underlying mechanics compared to simpler hashing schemes.

Conclusion

Extendible hashing provides a robust and efficient solution for managing dynamic datasets, particularly in scenarios requiring fast lookups. Its scalability, load balancing capabilities, and efficient data retrieval make it an attractive choice for database systems and other applications with evolving data requirements.

References

• Extendible Hashing - Wikipedia
• Extendible Hashing - GeeksforGeeks
• Extendible Hashing in Database Systems

Note: This article uses information from various sources on Github, including articles, code examples, and discussions. Credit is given to the original authors through the provided links.