Question

A file of 4096 blocks is to be sorted with an available buffer space of 64 blocks. How many passes will be needed in the merge phase of the external sort-merge algorithm?

Short answer

The merge phase of the external sort-merge algorithm will need 2 passes to sort a file of 4096 blocks with an available buffer space of 64 blocks.

Step-by-step solution

Calculating the Fan-Out

Firstly, calculate the fan-out of sorting process which is the number of blocks of the file that can be sorted in one pass. This can be calculated by dividing the total number of blocks by the available buffer space. In this case, the fan-out is \( \frac{4096}{64} = 64 \) which means 64 blocks can be sorted in one pass.

Determine the number of runs

Each pass creates a number of runs which can be merged in the following pass. With a fan-out of 64, 64 runs will be generated during the first pass.

Calculate the number of passes

Since each pass will merge fan-out number of runs, the total number of passes needed to merge all runs into a sorted sequence can be calculated with \( \lceil \log_{64}64 \rceil = 1 \) pass required to completely merge the file. This is added to the first pass, making it a total of 2 passes.

Key concepts

Database Sorting Techniques

Sorting is a fundamental operation in database management, vital for organizing and retrieving data efficiently. Among the many sorting techniques, the external sort-merge algorithm is a commonly used method, particularly for sorting large files that cannot fit entirely into main memory. This approach involves breaking the data into manageable 'runs', sorting these runs in memory, and then merging them into a single sorted list.

This process is composed of two main phases: the 'sorting phase' where runs are created and sorted, and the 'merge phase' where these sorted runs are combined. The algorithm is designed to optimize the use of available memory and disk I/O operations, leading to enhanced performance on large datasets. An intrinsic advantage of the external sort-merge is its ability to handle vast amounts of data beyond the limitations of physical RAM, making it a staple in database operations that require sorting huge files.

Block Storage

In the context of sorting and databases, block storage refers to the method of storing data in fixed-size blocks. Each block can be considered a 'page' of the database file system, and they are the fundamental units for data transfer between disk and memory.

When applying sorting algorithms like the external sort-merge, block storage is crucial because it dictates how data is read from and written to disk. Sorting algorithms benefit significantly from this structure, as it allows for efficient disk access patterns. By working with blocks, the algorithm can read and sort a block's worth of data at a time, ensuring that disk read and write operations are minimized, which is crucial since these operations are often bottlenecks in terms of performance.

Buffer Space Utilization

The concept of buffer space utilization is central to the efficiency of external sorting algorithms. Buffer space refers to the portion of the main memory reserved for holding the data blocks during the sorting process. In our example with 4096 blocks and 64 blocks of buffer space, the approach is to maximize the use of this limited buffer space to sort as much data as possible before writing it back to disk.

Good buffer management can drastically reduce the number of passes required to sort a file by increasing the 'fan-out'—the number of runs that can be merged in one pass. Efficient utilization of buffers ensures that each pass sorts and merges the maximum possible amount of data, thus reducing the total number of disk accesses and, consequently, the sorting time.