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Lecture 6 : Dynamic Hashing

Lecture 6 : Dynamic Hashing. Bong-Soo Sohn Assistant Professor School of Computer Science and Engineering Chung-Ang University. Dynamic Hashing. A hash table that grows to handle more items Virtual Hashing Dynamic Hashing Extendible Hashing Linear Hashing. Virtual Hashing.

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Lecture 6 : Dynamic Hashing

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  1. Lecture 6 : Dynamic Hashing Bong-Soo Sohn Assistant Professor School of Computer Science and Engineering Chung-Ang University

  2. Dynamic Hashing • A hash table that grows to handle more items • Virtual Hashing • Dynamic Hashing • Extendible Hashing • Linear Hashing

  3. Virtual Hashing • Use more than one hashing functions • Hash function : use modular function • H0 : address = key % N (N=2^0 X N) • # of buckets : N • Size of bucket : C • When overflow occurs • Related bucket is split • Different hash function is used. C+1 records are rehashed • Hj : address = key % (2^j X N ) , j=0, 1, 2, …

  4. Virtual Hashing Example Bucket 3 • N = 100, C = 4 • bucket 3 is full : [3, 103, 203, 303] • H0 = key % 100 • Overflow! when new record 403 is inserted • Use h1 = key % 200 and split bucket 3 3 103 203 303 3 203 403 103 303 Bucket 3 Bucket 103

  5. Virtual Hashing • Overflow when 603, 803 are inserted • Use h2 = key % 400 to split buckets • What happens? • When a key is searched, what hash function to apply? • Problems • How to handle the space between two split buckets?

  6. Dynamic hashing • # of buckets : N • Bucket size : C • We have indices pointing to each bucket • Example • N=20, C=3

  7. Dynamic Hashing • Use two functions • Hashing function H0 • obtain index entry # • Each index entry is corresponding to binary tree root • Determine which binary tree • Bit function B • convert key to Bit String (bit string size is controlled) • Decide which branch within each index binary tree

  8. Dynamic hashing algorithm • Convert key into index using H0 • Store a record in a bucket pointed by the index • If the bucket is full, split the bucket and make a binary tree and assign the record into appropriate binary tree node(bucket)

  9. Dynamic hashing • H0(key) determine binary tree root node • B(key) determine branch direction

  10. Dynamic hashing : example • B(key) • 0 : left , 1 : right

  11. Insert records 157, 95, 88, 205, 13

  12. Insert record 125 additionally

  13. Insert records 301, 6

  14. Design Project (due : Nov 12, 11:59pm) • Description • Design and implement your own dynamic hashing algorithm where hash table size can grow dynamically. • Submit 1 : Report • Your algorithm description including figures • Performance (compare with other trivial method such as re-hashing) • Show tables and graphs(plots) as much as possible. • Strength & weakness of your algorithm • Your report should be concise and easy to understand though it should contain essential information on your method and implementation • Submit 2 : source code • source code that includes your algorithm • When executing your code, the program should print detailed description on the events that occur in hash table for each operation.

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