A PARTS file with Part* as hash key includes records with...

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#.

Key Concepts

Average Cost Calculation in Hash-based Systems

Calculating the average cost in hash-based data retrieval involves assessing the expected number of block accesses needed per search. This incorporates understanding the distribution of records in buckets, the impact of collisions, and the efficiency of the underlying hash function in uniformly distributing keys.

Hash Function

A hash function is an algorithm that maps data, like keys, to fixed-size values, usually to serve as indices in data structures. It plays a critical role in organizing storage and retrieval, ensuring that data is distributed as evenly as possible to minimize collisions.

Modular Arithmetic

Modular arithmetic is used to constrain the output of a hash function within a fixed range. For instance, using the operation K mod 8 guarantees that the resulting hash values lie between 0 and 7, which aligns with the fixed number of storage buckets.

Bucket-based File Organization

Bucket-based file organization stores records in discrete blocks or buckets, with each bucket holding a limited number of records. This technique aids in managing disk access efficiently, as data can be retrieved by directly accessing the corresponding bucket based on the key's hash value.

Block Access and Retrieval Cost

Disk blocks, the fundamental units of data storage on physical disks, determine how data is read. The retrieval cost in a bucket-based organization is measured by the number of block accesses required to locate a record, highlighting the importance of an efficient hash function.

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