Post By: Hanan Mannan Contact Number: Pak (+92)-321-59-95-634 -------------------------------------------------------
DBMS Hashing
For a huge database structure it is not sometime feasible to search index through all its level and then reach the destination data block to retrieve the desired data. Hashing is an effective technique to calculate direct location of data record on the disk without using index structure.
It uses a function, called hash function and generates address when called with search key as parameters. Hash function computes the location of desired data on the disk.
Hash Organization
Bucket: Hash file stores data in bucket format. Bucket is considered a unit of storage. Bucket typically stores one complete disk block, which in turn can store one or more records.
Hash Function: A hash function h, is a mapping function that maps all set of search-keys K to the address where actual records are placed. It is a function from search keys to bucket addresses.
Static Hashing
In static hashing, when a search-key value is provided the hash function always computes the same address. For example, if mod-4 hash function is used then it shall generate only 5 values. The output address shall always be same for that function. The numbers of buckets provided remain same at all times.
[Image: Static Hashing]
Operation:
Insertion: When a record is required to be entered using static hash, the hash function h, computes the bucket address for search key K, where the record will be stored.
Bucket address = h(K)
Search: When a record needs to be retrieved the same hash function can be used to retrieve the address of bucket where the data is stored.
Delete: This is simply search followed by deletion operation.
BUCKET OVERFLOW:
The condition of bucket-overflow is known as collision. This is a fatal state for any static hash function. In this case overflow chaining can be used.
Overflow Chaining: When buckets are full, a new bucket is allocated for the same hash result and is linked after the previous one. This mechanism is called Closed Hashing.
[Image: Overflow chaining]
Linear Probing: When hash function generates an address at which data is already stored, the next free bucket is allocated to it. This mechanism is called Open Hashing.
[Image: Linear Probing]
For a hash function to work efficiently and effectively the following must match:
Distribution of records should be uniform
Distribution should be random instead of any ordering
Dynamic Hashing
Problem with static hashing is that it does not expand or shrink dynamically as the size of database grows or shrinks. Dynamic hashing provides a mechanism in which data buckets are added and removed dynamically and on-demand. Dynamic hashing is also known as extended hashing.
Hash function, in dynamic hashing, is made to produce large number of values and only a few are used initially.
[Image: Dynamic Hashing]
ORGANIZATION
The prefix of entire hash value is taken as hash index. Only a portion of hash value is used for computing bucket addresses. Every hash index has a depth value, which tells it how many bits are used for computing hash function. These bits are capable to address 2n buckets. When all these bits are consumed, that is, all buckets are full, then the depth value is increased linearly and twice the buckets are allocated.
OPERATION
Querying: Look at the depth value of hash index and use those bits to compute the bucket address.
Update: Perform a query as above and update data.
Deletion: Perform a query to locate desired data and delete data.
Insertion: compute the address of bucket
If the bucket is already full
Add more buckets
Add additional bit to hash value
Re-compute the hash function
Else
Add data to the bucket
If all buckets are full, perform the remedies of static hashing.
Hashing is not favorable when the data is organized in some ordering and queries require range of data. When data is discrete and random, hash performs the best.
Hashing algorithm and implementation have high complexity than indexing. All hash operations are done in constant time.
Post By: Hanan Mannan Contact Number: Pak (+92)-321-59-95-634 -------------------------------------------------------
DBMS Indexing
We know that information in the DBMS files is stored in form of records. Every record is equipped with some key field, which helps it to be recognized uniquely.
Indexing is a data structure technique to efficiently retrieve records from database files based on some attributes on which the indexing has been done. Indexing in database systems is similar to the one we see in books.
Indexing is defined based on its indexing attributes. Indexing can be one of the following types:
Primary Index: If index is built on ordering 'key-field' of file it is called Primary Index. Generally it is the primary key of the relation.
Secondary Index: If index is built on non-ordering field of file it is called Secondary Index.
Clustering Index: If index is built on ordering non-key field of file it is called Clustering Index.
Ordering field is the field on which the records of file are ordered. It can be different from primary or candidate key of a file.
Ordered Indexing is of two types:
Dense Index
Sparse Index
Dense Index
In dense index, there is an index record for every search key value in the database. This makes searching faster but requires more space to store index records itself. Index record contains search key value and a pointer to the actual record on the disk.
[Image: Dense Index]
Sparse Index
In sparse index, index records are not created for every search key. An index record here contains search key and actual pointer to the data on the disk. To search a record we first proceed by index record and reach at the actual location of the data. If the data we are looking for is not where we directly reach by following index, the system starts sequential search until the desired data is found.
[Image: Sparse Index]
Multilevel Index
Index records are comprised of search-key value and data pointers. This index itself is stored on the disk along with the actual database files. As the size of database grows so does the size of indices. There is an immense need to keep the index records in the main memory so that the search can speed up. If single level index is used then a large size index cannot be kept in memory as whole and this leads to multiple disk accesses.
[Image: Multi-level Index]
Multi-level Index helps breaking down the index into several smaller indices in order to make the outer most level so small that it can be saved in single disk block which can easily be accommodated anywhere in the main memory.
B+ Tree
B tree is multi-level index format, which is balanced binary search trees. As mentioned earlier single level index records becomes large as the database size grows, which also degrades performance.
All leaf nodes of B+ tree denote actual data pointers. B+ tree ensures that all leaf nodes remain at the same height, thus balanced. Additionally, all leaf nodes are linked using link list, which makes B+ tree to support random access as well as sequential access.
STRUCTURE OF B+ TREE
Every leaf node is at equal distance from the root node. A B+ tree is of order n where n is fixed for every B+ tree.
[Image: B+ tree]
Internal nodes:
Internal (non-leaf) nodes contains at least ⌈n/2⌉ pointers, except the root node.
At most, internal nodes contain n pointers.
Leaf nodes:
Leaf nodes contain at least ⌈n/2⌉ record pointers and ⌈n/2⌉ key values
At most, leaf nodes contain n record pointers and n key values
Every leaf node contains one block pointer P to point to next leaf node and forms a linked list.
B+ TREE INSERTION
B+ tree are filled from bottom. And each node is inserted at leaf node.
If leaf node overflows:
Split node into two parts
Partition at i = ⌊(m+1)/2⌋
First i entries are stored in one node
Rest of the entries (i+1 onwards) are moved to a new node
ith key is duplicated in the parent of the leaf
If non-leaf node overflows:
Split node into two parts
Partition the node at i = ⌈(m+1)/2⌉
Entries upto i are kept in one node
Rest of the entries are moved to a new node
B+ TREE DELETION
B+ tree entries are deleted leaf nodes.
The target entry is searched and deleted.
If it is in internal node, delete and replace with the entry from the left position.
After deletion underflow is tested
If underflow occurs
Distribute entries from nodes left to it.
If distribution from left is not possible
Distribute from nodes right to it
If distribution from left and right is not possible
