Extendible hashing

Introduction and Overview of Extendible Hashing - Extendible Hashing is a fast access method for dynamic files. - It is a hash-based indexing technique. - It allows for efficient insertion and retrieval of data. - The hash function returns a string of bits. - The first i bits of each string are used as indices to determine the location in the directory (hash table). Key Insertion, Bucket Overflow, and Directory Organization - Keys are inserted into the hash table based on their hashed values. - If a bucket becomes full, it needs to be split. - The local depth of a bucket determines the number of bits used for hashing. - If the local depth is equal to the global depth, the directory needs to be doubled. - If the local depth is less than the global depth, the bucket can be split without doubling the directory. - The directory contains pointers to buckets. - The global depth represents the number of bits used for hashing in the directory. - The local depth represents the number of bits used for hashing in a bucket. - After a bucket split, the local depth is incremented and used for redistributing the entries. - The directory size is doubled when a bucket becomes full. Example Implementation in Python - The extendible hashing algorithm can be implemented in Python. - The code uses the least significant bits for efficient table expansion. - The directory is represented as a list of pages. - Each page has a map of key-value pairs and a local depth. - The get_page() function retrieves the page based on the hashed key. - The put() function inserts a key-value pair into the appropriate page. Advantages and Limitations of Extendible Hashing - Extendible Hashing allows for efficient insertion and retrieval of data. - It handles dynamic file sizes effectively. - It provides a balanced distribution of keys across buckets. - However, the depth cannot exceed the bit size of an integer. - Doubling the directory or splitting a bucket may not allow entries to be rehashed to different buckets. Performance and Comparison with Other Hashing Techniques - Extendible hashing provides efficient search, insert, and delete operations. - The directory structure allows for a balanced distribution of records. - The number of disk accesses is minimized for most operations. - The performance remains stable even with a large number of records. - The space overhead of the directory structure is relatively small. - Extendible hashing is more flexible than static hashing. - It handles dynamic changes in the number of records effectively. - Compared to linear hashing, extendible hashing has a simpler structure. - Extendible hashing performs well in scenarios with frequent updates. - Other hashing techniques may be more suitable for specific use cases.