Odd–even sort

Odd–even sort

Example of odd-even transposition sort sorting a list of random numbers.
Class	Sorting algorithm
Data structure	Array
Worst case performance	O(n2)

In computing, an odd–even sort or odd–even transpostion sort (also known as brick sort^[1]) is a relatively simple sorting algorithm, developed originally for use on parallel processors with local interconnections. It is a comparison sort related to bubble sort, with which it shares many characteristics. It functions by comparing all (odd, even)-indexed pairs of adjacent elements in the list and, if a pair is in the wrong order (the first is larger than the second) the elements are switched. The next step repeats this for (even, odd)-indexed pairs (of adjacent elements). Then it alternates between (odd, even) and (even, odd) steps until the list is sorted.

Sorting on processor arrays

On parallel processors, with one value per processor and only local left–right neighbor connections, the processors all concurrently do a compare–exchange operation with their neighbors, alternating between odd–even and even–odd pairings. This algorithm was originally presented, and shown to be efficient on such processors, by Habermann in 1972.^[2]

The algorithm extends efficiently to the case of multiple items per processor. In the Baudet–Stevenson odd–even merge-splitting algorithm, each processor sorts its own sublist at each step, using any efficient sort algorithm, and then performs a merge splitting, or transposition–merge, operation with its neighbor, with neighbor pairing alternating between odd–even and even–odd on each step.^[3]

Batcher's odd–even mergesort

A related but more efficient sort algorithm is the Batcher odd–even mergesort, using compare–exchange operations and perfect-shuffle operations.^[4] Batcher's method is efficient on parallel processors with long-range connections.^[5]

Algorithm

The single-processor algorithm, like bubblesort, is simple but not very efficient. Here a zero-based index is assumed:

/* Assumes a is an array of values to be sorted. */
var sorted = false;
while(!sorted)
{
    sorted=true;
    for(var i = 1; i < list.length-1; i += 2)
    {
        if(a[i] > a[i+1])
        {
            swap(a, i, i+1);
            sorted = false;
        }
    }
 
    for(var i = 0; i < list.length-1; i += 2)
    {
        if(a[i] > a[i+1])
        {
            swap(a, i, i+1);
            sorted = false;
        }
    }
}

References

1. ^ Phillips, Malcolm. Sort Techniques "Array Sorting". http://homepages.ihug.co.nz/~aurora76/Malc/Sorting_Array.htm#Exchanging Sort Techniques. Retrieved 3 August 2011. 
2. ^ N. Haberman (1972) "Parallel Neighbor Sort (or the Glory of the Induction Principle)," CMU Computer Science Report (available as Technical report AD-759 248, National Technical Information Service, US Department of Commerce, 5285 Port Royal Rd Sprigfield VA 22151).
3. ^ S. Lakshmivarahan, S. K. Dhall, and L. L. Miller (1984), Franz L. Alt and Marshall C. Yovits, ed., "Parallel Sorting Algorithms", Advances in computers (Academic Press) 23: 295–351, ISBN 9780120121236, http://books.google.com/books?id=Mo2Q-TEwKGUC&pg=PA322 
4. ^ Robert Sedgewick (2003). Algorithms in Java, Parts 1-4 (3rd ed.). Addison-Wesley Professional. pp. 454–464. ISBN 9780201361209. http://books.google.com/books?id=hyvdUQUmf2UC&pg=PA455. 
5. ^ Allen Kent and James G. Williams (1993). Encyclopedia of Computer Science and Technology: Supplement 14. CRC Press. p. 33–38. ISBN 9780824722821. http://books.google.com/books?id=F9Y4oZ9qZnYC&pg=PA33.