External Sorting of a 4.6 GB File with 500 Million Integers: Strategies and Implementation

The problem presents a 4.6 GB file named bigdata containing 500 million random integers, each on a separate line, and asks how to sort it.

Initial attempts at internal sorting include a three‑way quicksort implementation and a merge sort, both with cutoff thresholds for small sub‑arrays and using insertion sort for those cases. Code snippets illustrate the algorithms.

private final int cutoff = 8;

public
void perform(Comparable
[] a) {
    perform(a,0,a.length - 1);
}

private
int median3(Comparable
[] a,int x,int y,int z) {
    if(lessThan(a[x],a[y])) {
        if(lessThan(a[y],a[z])) {
            return y;
        } else if(lessThan(a[x],a[z])) {
            return z;
        } else {
            return x;
        }
    } else {
        if(lessThan(a[z],a[y])){
            return y;
        } else if(lessThan(a[z],a[x])) {
            return z;
        } else {
            return x;
        }
    }
}

private
void perform(Comparable
[] a,int low,int high) {
    int n = high - low + 1;
    if(n <= cutoff) {
        InsertionSort insertionSort = SortFactory.createInsertionSort();
        insertionSort.perform(a,low,high);
    } else if(n <= 100) {
        int m = median3(a,low,low + (n >>> 1),high);
        exchange(a,m,low);
    } else {
        int gap = n >>> 3;
        int m = low + (n >>> 1);
        int m1 = median3(a,low,low + gap,low + (gap << 1));
        int m2 = median3(a,m - gap,m,m + gap);
        int m3 = median3(a,high - (gap << 1),high - gap,high);
        int ninther = median3(a,m1,m2,m3);
        exchange(a,ninther,low);
    }
    if(high <= low) return;
    int lt = low;
    int gt = high;
    Comparable
pivot = a[low];
    int i = low + 1;
    while(i <= gt) {
        if(lessThan(a[i],pivot)) {
            exchange(a,lt++,i++);
        } else if(lessThan(pivot,a[i])) {
            exchange(a,i,gt--);
        } else {
            i++;
        }
    }
    perform(a,low,lt - 1);
    perform(a,gt + 1,high);
}

Running the Unix sort -n bigdata -o bigdata.sorted command completes in about 24 minutes, but the author notes high I/O, memory pressure, and CPU time spent on context switches.

A bitmap‑based sorting method is then described, using a BitSet to record the presence of each integer, reading the large file into memory, setting bits, and then writing out the sorted numbers in ascending or descending order. This approach finishes in roughly 190 seconds on a machine with 4.6 GB/32 GB memory.

private BitSet bits;

public void perform(String largeFileName,int total,String destLargeFileName,Castor
castor,int readerBufferSize,int writerBufferSize,boolean asc) throws IOException {
    System.out.println("BitmapSort Started.");
    long start = System.currentTimeMillis();
    bits = new BitSet(total);
    InputPart
largeIn = PartFactory.createCharBufferedInputPart(largeFileName, readerBufferSize);
    OutputPart
largeOut = PartFactory.createCharBufferedOutputPart(destLargeFileName, writerBufferSize);
    largeOut.delete();
    Integer data;
    int off = 0;
    while(true) {
        data = largeIn.read();
        if(data == null) break;
        int v = data;
        set(v);
        off++;
    }
    largeIn.close();
    int size = bits.size();
    System.out.println(String.format("lines : %d ,bits : %d", off, size));
    if(asc) {
        for(int i = 0; i < size; i++) {
            if(get(i)) {
                largeOut.write(i);
            }
        }
    } else {
        for(int i = size - 1; i >= 0; i--) {
            if(get(i)) {
                largeOut.write(i);
            }
        }
    }
    largeOut.close();
    long stop = System.currentTimeMillis();
    long elapsed = stop - start;
    System.out.println(String.format("BitmapSort Completed.elapsed : %dms",elapsed));
} 

private void set(int i) { bits.set(i); }
private boolean get(int v) { return bits.get(v); }

Finally, an external sorting strategy is detailed for environments with limited memory. The file is processed in chunks: each chunk is read into a small buffer, internally sorted, and written to temporary sorted part files. Afterwards, a multi‑way merge reads the smallest elements from each part file and writes them to the final sorted output. The complete external sort runs in about 13 minutes.