Question

Suppose that we have a hash file of fixed-length records, and suppose that overflow is handled by chaining. Outline algorithms for insertion, deletion, and modification of a file record. State any assumptions you make.

Short answer

Insertion in a hash file involves computing bucket based on hash value of key and then placing record in this bucket or overflow chain. Deletion requires locating the target record through its hash value and removing it from its bucket or overflow chain, while reordering remaining records. Modification requires searching for the record, making necessary changes, and reinserting it (if key changes) or modifying it in place (if key remains unchanged).

Step-by-step solution

Algorithm for Insertion

First, calculate the hash value of the input record's key, which will provide the address of the bucket where this record should be inserted. Next, inspect the selected bucket. If it still has space, place the record in it. However, if it's full, add the record to the overflow chain associated with the bucket.

Algorithm for Deletion

Just like with insertion, start by finding the bucket that should contain the record that is to be deleted, by using the hash function. Browse the records in the mentioned bucket and its overflow chain until the required record is found. If the record isn't in either the bucket or the overflow chain, it means the record doesn't exist in the hash file. If the record is found, delete it and rearrange the records as needed. Consider whether the overflow chain can be shortened or even removed.

Algorithm for Modification

To modify a record, calculate the hash value of the record's key to specify the appropriate bucket. Search the bucket and its overflow chain for the record. If it couldn't be located, it then implies that the record does not exist. If the record is found, change the value of the record accordingly to complete the modification process. If the modification involves a key change, it may be necessary to relocate the record. In this case, delete the record first, modify it, then reinsert it back into the hash file using the insertion algorithm mentioned earlier.

Key concepts

Chaining Method

In a database, the chaining method is a way to handle situations where two records have the same hash value, ultimately leading to a 'collision'. Hashing in databases means each record is assigned a "home" location via a hash function. When two records are directed to the same home location, the chaining method helps manage this challenge smoothly.
Think of it as creating a linked list of records, forming a 'chain'. When a collision occurs, if there’s already a record in the calculated spot, the new record is added to a list associated with the original spot.
This means the overflow records aren't all over the place, but neatly organized behind their home location. It’s efficient because:

• It keeps data organized and easy to track.
• It minimizes search time when accessing records, even if they’re in the overflow area.
• It’s easy to implement by just maintaining an additional pointer for the records in overflow.

Using a chaining method ensures that regardless of how many collisions occur, the hash file remains organized and manageable.

File Record Insertion

Inserting a record using the chaining method starts by calculating the hash value of the record’s key, directing you to the correct bucket. The bucket acts like a home base for the record. If there's enough space in the bucket, the record is directly inserted there. But, what if the bucket is full?
This is where chaining shines. If the bucket is full, add the record to the overflow chain associated with that bucket, expanding the chain with a new link. Some benefits of this method are:

• Even when the primary bucket is full, new records can still be stored by linking them in the overflow chain.
• The structure of the data file is maintained, avoiding the need to shift data around to accommodate new entries.
• The insertion becomes simpler and computationally inexpensive as it leverages linked lists for overflow.

This process allows for continuous data growth and efficient management of records despite collisions.

File Record Deletion

File record deletion follows a similar principle to insertion. It starts by using the hash function to find the correct bucket where the record should be located. The deletion process effectively removes the record from either the bucket or its overflow chain. Here's how it works step-by-step:
First, locate the bucket and any associated overflow chain by using the hash function. then, scan through the records until the desired record is identified.
If you find what you're looking for, remove it and adjust the links in the chain to 'bypass' the removed record, keeping the chain intact.
If the record is part of a chain, check if removing it can also allow you to collapse part of the overflow chain, reducing its length. This can keep the file more organized and efficient.
This approach ensures that:

• Deleted records do not disrupt the continuity of the chain.
• The space utilized by overflow records is optimized.
• Finding and removing records can be done swiftly without an exhaustive reorganization.

By maintaining the integrity of the chain during deletions, the organization of data remains precise and interconnected.

File Record Modification

Modifying a file record could be straightforward or complex based on whether the record's key, which determines its hash value, changes during the modification. Here's how you go about this task:
First, compute the hash value for the record's key to identify the appropriate bucket. Then, search for the record in the bucket and its overflow chain.
If you locate the record and only need to update its value, proceed with the modification directly.
However, if the modification changes the record's key, the process becomes slightly more complex as the record's location might need adjusting. In these cases:

• Delete the record from the current bucket or overflow chain using the deletion method.
• Make the necessary modifications to the record that includes changing the key.
• Reinsert the modified record using the file record insertion method to ensure it's stored in the correct location according to the new key.

This ensures that despite changes to a record’s key or value, the integrity and organization of the database are maintained optimally.