Question

A PARTS file with Part* as hash key includes records with the following Part* val. ues: 2369,3760,4692,4871,5659,1821,1074,7115,1620,2428,3943,4750 \(6975,4981,9208 .\) The file uses eight buckets, numbered 0 to 7. Each bucket is one disk block and holds two records. Load these records into the file in the given order, using the hash function \(h(K)=K \bmod 8 .\) Calculate the average number of block accesses for a random retrieval on Part#.

Short answer

To calculate the average number of block accesses, apply the hash function to distribute the records into the buckets. Calculate the block accesses for each bucket as 1 plus half the number of overflow records. Finally, sum up the block accesses for all buckets and divide by the total number of buckets.

Step-by-step solution

Understand Hashing

Hash function assigns each record to a specific bucket, based on the record's key value. In this case, given hash function is \(h(K) = K \bmod 8\), where K represents the Part# value.

Apply Hash Function

Apply hash function to each Part# value to distribute records into the buckets. For example, for Part# '2369', the bucket# will be \(2369 \bmod 8 = 1\). Repeat this process for all Part# values.

Distribution in Buckets

Once hash function is applied to all Part# values, we have the bucket distribution. Remember that each bucket has a capacity of two records, so any overflow must be managed accordingly.

Calculate Average Block Accesses

The average number of block accesses for a random retrieval is the sum of the number of block accesses for each bucket divided by the total number of buckets. The number of block accesses for a bucket is 1 plus half the number of overflow records.

Key concepts

Hash Function

In the world of databases, a hash function is a crucial component for efficiently managing data. It acts as a mathematical algorithm that transforms a search key, often referred to as the 'hash key,' into a specific value known as the 'hash value.' These hash values are used to determine the location, or bucket, where the records should be stored inside the database.

To understand this better, visualize it as a librarian putting away books using a special code. The magic formula that converts a book's title into this code is the hash function. In the given exercise, our books are records, and our titles are Part# values. The special code is established using the formula h(K) = K mod 8, where K represents the Part# value. As a result of this operation, any Part# value will be directed to one of the eight available buckets in the system.

Why is this useful? Well, it optimizes the process of data retrieval. Instead of scanning an entire database, one needs only to look in the specific bucket where the data is placed. By doing so, the search becomes much faster -- akin to knowing exactly which shelf to search for that one book in a massive library. However, the efficiency of a hash function depends on how well it distributes the data across the available buckets, which is crucial for preventing what we call 'collisions' where multiple records end up in the same spot.

Bucket Distribution

Moving on to bucket distribution, it refers to how the records are allocated among the available buckets after being processed by the hash function. Good bucket distribution means that the records are spread out evenly, which in turn minimizes the chances of 'collisions' -- when multiple records are assigned to the same bucket.

Let's apply this to our exercise. Our 'librarian' hash function sends each Part# to one of eight 'shelves' (buckets), each designed to hold only two 'books' (records). If more than two books end up on the same shelf, we have a situation of overflow, which needs to be managed. In databases, overflow can be handled in various ways, such as chaining or open addressing. But regardless of the method, the goal is to maintain the efficiency of retrieval.

Ensuring Even Distribution

In practice, ensuring an even distribution of data across buckets is a critical task. The hash function must be designed to reduce the likelihood of clustering, which occurs when a disproportionate number of records hash to the same bucket. This is important because poor distribution could lead to a degradation of performance, making data access much slower, akin to a traffic jam in one aisle of the library while others are empty.

Average Block Access

Lastly, the concept of average block access is a measure of the database's retrieval efficiency. In the context of our exercise, a block refers to a single bucket of the database. The average block access is the average number of times the system must read a block to retrieve a random record.

In simple terms, it's like the average number of guesses you have to make before you pick the correct 'book' (record) from the 'shelf' (bucket). Imagine you randomly pick a shelf in the library to find a book. If books are evenly distributed, you'll guess right faster. In the case where there's a cluster of books on one shelf -- you'll probably guess more times.

To calculate the average block access in our scenario, we consider how many times each block might be accessed to retrieve a record and then average that out over all the blocks. The formula takes into account the main access to the bucket and the additional accesses required if there are any overflow records. In real-world databases, this metric is crucial because it's tied directly to the time it takes for a user or application to retrieve data. Maintaining a low average block access is often a major goal in database optimization -- it's what keeps the 'customers' of the 'library' happy and coming back.