Lecture 6 : Dynamic Hashing

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 (N20 X N)
• of buckets N
• Size of bucket C
• When overflow occurs
• Related bucket is split
• Different hash function is used. C1 records are
  rehashed
• Hj address key (2j X N ) , j0, 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
• N20, C3

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, 1159pm)

• 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.