How external merge sort algorithm works?

Demystifying External Merge Sort: Handling Massive Datasets

Explore the intricacies of the external merge sort algorithm, a powerful technique for sorting datasets that are too large to fit into main memory. Learn its phases, components, and practical applications.

Sorting is a fundamental operation in computer science, but what happens when the dataset you need to sort exceeds the available RAM? Traditional in-memory sorting algorithms like quicksort or heapsort become impractical. This is where external sorting algorithms come into play, designed to handle data residing on slower external storage devices like hard drives. Among these, external merge sort stands out as a robust and widely used solution. This article will break down how external merge sort works, its core phases, and why it's crucial for big data processing.

The Challenge of External Sorting

Before diving into the algorithm, it's important to understand the challenge. When data doesn't fit in memory, I/O operations (reading from disk, writing to disk) become the bottleneck. These operations are orders of magnitude slower than CPU operations. An efficient external sorting algorithm must minimize disk I/O. External merge sort achieves this by breaking the problem into smaller, manageable chunks that can be sorted in memory, and then intelligently merging these sorted chunks.

The core challenge: Data exceeds RAM capacity

Phase 1: Run Creation (Sorting Sub-Files)

The first phase of external merge sort is called 'run creation' or 'sorting sub-files'. The large input file is divided into smaller chunks, each of which can fit into the available main memory. Each chunk is then sorted independently using a conventional in-memory sorting algorithm (like quicksort or heapsort). The sorted chunks, known as 'runs', are then written back to disk. The size of each run is limited by the amount of available RAM. For example, if you have 1GB of RAM and your file is 10GB, you'll create 10 runs, each 1GB in size.

import os

def sort_in_memory(chunk):
    # In-memory sort (e.g., Timsort in Python)
    return sorted(chunk)

def create_runs(input_filepath, run_size_mb, output_dir):
    chunk_size = run_size_mb * 1024 * 1024 # Convert MB to bytes
    run_count = 0
    with open(input_filepath, 'rb') as infile:
        while True:
            chunk = infile.read(chunk_size)
            if not chunk:
                break
            
            # Assuming chunk contains records that can be sorted
            # For simplicity, let's assume records are newline-separated strings
            records = chunk.decode('utf-8').splitlines()
            sorted_records = sort_in_memory(records)
            
            run_filepath = os.path.join(output_dir, f'run_{run_count}.txt')
            with open(run_filepath, 'w', encoding='utf-8') as outfile:
                outfile.write('\n'.join(sorted_records))
            run_count += 1
    print(f'Created {run_count} runs.')

# Example usage:
# create_runs('large_data.txt', 100, 'temp_runs/')

Simplified Python example for the run creation phase. It reads data in chunks, sorts each chunk in memory, and writes it to a new run file.

Phase 2: Multi-Way Merge

Once all runs are created and written to disk, the second phase, 'multi-way merge', begins. This phase repeatedly merges the sorted runs until a single, fully sorted file is produced. The merging process typically works by taking K runs at a time, where K is limited by the number of available file handles and memory buffers. For each merge step, one block of data is read from each of the K runs into input buffers in memory. A K-way merge algorithm (often implemented using a min-priority queue) then continuously picks the smallest element from all K input buffers, writes it to an output buffer, and then refills the buffer from which the element was taken. When the output buffer is full, it's written to disk as a new, larger sorted run.

Visualizing the multi-way merge process

import heapq
import os

def merge_k_runs(run_files, output_filepath):
    # Open all run files for reading
    file_handles = [open(f, 'r', encoding='utf-8') for f in run_files]
    
    # Use a min-priority queue to keep track of the smallest element from each run
    # Each item in the heap is (value, file_index, file_handle)
    min_heap = []
    for i, fh in enumerate(file_handles):
        line = fh.readline()
        if line:
            heapq.heappush(min_heap, (line.strip(), i, fh))
            
    with open(output_filepath, 'w', encoding='utf-8') as outfile:
        while min_heap:
            smallest_val, file_idx, fh = heapq.heappop(min_heap)
            outfile.write(smallest_val + '\n')
            
            # Read the next line from the file this value came from
            next_line = fh.readline()
            if next_line:
                heapq.heappush(min_heap, (next_line.strip(), file_idx, fh))
                
    # Close all file handles
    for fh in file_handles:
        fh.close()
    print(f'Merged {len(run_files)} runs into {output_filepath}.')

# Example usage (assuming 'temp_runs/' contains run_0.txt, run_1.txt, etc.):
# run_files = [os.path.join('temp_runs', f) for f in os.listdir('temp_runs') if f.startswith('run_')]
# merge_k_runs(run_files, 'final_sorted_data.txt')

Simplified Python example demonstrating a K-way merge using a min-priority queue.

Optimizations and Considerations

Several optimizations can enhance the performance of external merge sort:

• Replacement Selection (Natural Merging): Instead of fixed-size runs, replacement selection can create longer runs by intelligently using memory. It uses a min-priority queue to output the smallest element, and if the next element read from input is greater than or equal to the last outputted element, it's added to the current run. Otherwise, it starts a new run. This often results in runs that are twice the size of memory on average.
• Buffer Management: Efficiently managing input and output buffers is critical to minimize disk seeks and maximize throughput. Reading larger blocks of data at once reduces the number of I/O calls.
• Multi-level Merging: If the number of initial runs is very large, a single K-way merge might not be enough. You might perform several passes of K-way merges, gradually reducing the number of runs until only one remains. For example, merge 100 runs into 10 larger runs, then merge those 10 into 1 final run.
• Parallelism: Modern systems can leverage multiple cores or machines to parallelize both the run creation and the merging phases, significantly speeding up the sorting process.

1. Step 1

Determine Available Memory: Identify the maximum amount of RAM you can dedicate to sorting. This dictates the size of your initial runs and the number of runs you can merge simultaneously.

2. Step 2

Implement Run Creation: Write code to read data in chunks, sort each chunk in memory, and write the sorted chunks (runs) to temporary files on disk.

3. Step 3

Implement K-Way Merge: Develop a K-way merge function that takes multiple sorted run files as input and produces a single, larger sorted run file. Use a min-priority queue to efficiently find the next smallest element across all input buffers.

4. Step 4

Orchestrate Merge Passes: If the number of initial runs is greater than K, repeatedly apply the K-way merge until all runs are consolidated into a single sorted output file. This might involve creating intermediate directories for temporary merge results.

5. Step 5

Clean Up Temporary Files: After the final sorted file is generated, ensure all temporary run files are deleted to free up disk space.

External merge sort is a cornerstone algorithm in big data processing, database management systems, and operating systems. Its ability to efficiently handle datasets exceeding memory capacity makes it indispensable for tasks ranging from sorting massive log files to building search indexes. By understanding its two core phases – run creation and multi-way merge – along with its various optimizations, you gain valuable insight into how large-scale data challenges are tackled in practice.