Download presentation

Presentation is loading. Please wait.

Published byKaterina Dowler Modified over 2 years ago

1
Hash Tables Hash function h: search key [0…B-1]. Buckets are blocks, numbered [0…B-1]. Big idea: If a record with search key K exists, then it must be in bucket h(K). - Cuts search down by a factor of B. - One disk I/O if there is only one block per bucket. HashTable Lookup: For record(s) with search key K, compute h(K); search that bucket.

2
HashTable Insertion Put in bucket h(K) if it fits; otherwise create an overflow block. - Overflow block(s) are part of bucket. Example: Insert record with search key g.

3
What if the File Grows too Large? Efficiency is highest if #records < #buckets #(records/block) If file grows, we need a dynamic hashing method to maintain the above relationship. - Extensible Hashing: double the number of buckets when needed. - Linear hashing: add one more bucket as appropriate.

4
Dynamic Hashing Framework Hash function h produces a sequence of k bits. Only some of the bits are used at any time to determine placement of keys in buckets. Extensible Hashing (Buckets may share blocks!) Keep parameter i = number of bits from the beginning of h(K) that determine the bucket. Bucket array now = pointers to buckets. - A block can serve as several buckets. - For each block, a parameter j i tells how many bits of h(K) determine membership in the block. - I.e., a block represents 2 i-j buckets that share the first j bits of their number.

5
Example An extensible hash table when i=1:

6
Extensible Hashtable Insert If record with key K fits in the block pointed to by h(K), put it there. If not, let this block B represent j bits. 1. j

7
Example Insert record with h(K) = 1010. Before Now, after the insertion

8
Example: Next Next: records with h(K)=0000; h(K)=0111. - Bucket for 0... gets split, - but i stays at 2. Then: record with h(K) = 1000. - Overflows bucket for 10... - Raise i to 3. After the insertions Currently

9
Extensible Hash Tables: Advantages: Lookup; never search more than one data block. - Hope that the bucket array fits in main memory Defects: Substantial amount of work to double the bucket array - Interrupts access to data file - Makes certain insertions appear to take very long Doubling the bucket array soon is going to make the array to not fit in main memory. Problem with skewed key distributions. - E.g. Let 1 block=2 records. Suppose that three records have hash values, which happen to be the same in the first 20 bits. - In that case we would have i=20 and and one million bucket- array entries, even though we have only 3 records!!

10
Linear Hashing Use i bits from right (loworder) end of h(K). Buckets numbered [0…n-1], where 2 i-1

11
Linear HashTable Insert Pick an upper limit on capacity, - e.g., 85% (1.7 records/bucket in our example). If an insertion exceeds capacity limit, set n := n + 1. - If new n is 2 i + 1, set i := i + 1. No change in bucket numbers needed --- just imagine a leading 0. - Need to split bucket n - 2 i-1 because there is now a bucket numbered (old) n.

12
Example Insert record with h(K) = 0101. - Capacity limit exceeded; increment n. r=3 n=2 i=1 #of records #of buckets r=4 n=3 i=2 #of records #of buckets

13
Example Insert record with h(K) = 0001. - Capacity limit not exceeded. - But bucket is full; add overflow bucket. r=5 n=3 i=2

14
Example Insert record with h(K) = 1100. - Capacity exceeded; set n = 4, add bucket 11. - Split bucket 01. r=7 n=4 i=2

15
Lookup in Linear Hash Table For record(s) with search key K, compute h(K); search the corresponding bucket according to the procedure described for insertion. If the record we wish to look up isn’t there, it can’t be anywhere else. E.g. lookup for a key which hashes to 1010, and then for a key which hashes to 1011. r=4 n=3 i=2

16
Exercise Suppose we want to insert keys with hash values: 0000…1111 in a linear hash table with 100% capacity threshold. Assume that a block can hold three records.

Similar presentations

OK

Static Hashing (using overflow for collision managment e.g., h(key) mod M h key Primary bucket pages 1 0 M-1 Overflow pages(as separate link list) Overflow.

Static Hashing (using overflow for collision managment e.g., h(key) mod M h key Primary bucket pages 1 0 M-1 Overflow pages(as separate link list) Overflow.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on plants for grade 4 Ppt on two point perspective buildings Ppt on bluetooth and wifi Ppt on network security threats Ppt on save environment paintings Product mix ppt on nestle chocolate Ppt on as 14 amalgamation of companies Download ppt on mind controlled robotic arms manufacturing Ppt on column chromatography steps Ppt on role of individual in conservation of natural resources