viff

changeset 877:f12a36276d56

Described the complexity of the bitonic sort.
author Martin Geisler <mg@daimi.au.dk>
date Fri, 08 Aug 2008 10:23:14 +0200
parents 3d13185afed2
children f39882ce0e89
files apps/sort.py
diffstat 1 files changed, 21 insertions(+), 0 deletions(-) [+]
line diff
     1.1 --- a/apps/sort.py	Fri Aug 08 10:18:10 2008 +0200
     1.2 +++ b/apps/sort.py	Fri Aug 08 10:23:14 2008 +0200
     1.3 @@ -17,6 +17,27 @@
     1.4  # You should have received a copy of the GNU Lesser General Public
     1.5  # License along with VIFF. If not, see <http://www.gnu.org/licenses/>.
     1.6  
     1.7 +# This example demonstrates how a secure sorting algorithm can be
     1.8 +# implemented using VIFF. The algorithm used is bitonic sort which was
     1.9 +# chosen in order to maximize the amount of work (comparisons) done in
    1.10 +# parallel. Bitonic sort uses 1/2 * log n * (log n + 1) comparator
    1.11 +# stages and each stage consists of n/2 parallel comparisons. The
    1.12 +# total number of comparisons is thus in O(n log^2 n).
    1.13 +#
    1.14 +# This is larger than the lower bound of O(n log n) for comparison
    1.15 +# based sorting algorithms, achieved by mergesort and other well known
    1.16 +# algorithms. The problem with mergesort is its merging step: to merge
    1.17 +# two sorted arrays of length n/2 one needs up to n comparisons, and
    1.18 +# what is worse, the comparisons must be made one after another. The
    1.19 +# mergesort does one merge with lists of size n/2, two merges with
    1.20 +# lists of size n/4, and so on. This gives a total chain of
    1.21 +# comparisons of length n + n/2 + n/4 + ... + 1 = 2n - 1, which is
    1.22 +# more than the O(log^2 n) stages needed by the Bitonic Sort.
    1.23 +#
    1.24 +# See this page for more analysis and a Java implementation:
    1.25 +#
    1.26 +# http://iti.fh-flensburg.de/lang/algorithmen/sortieren/bitonic/bitonicen.htm
    1.27 +
    1.28  # Give a player configuration file as a command line argument or run
    1.29  # the example with '--help' for help with the command line options.
    1.30