Mercurial > 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(-) [+] |
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--- a/apps/sort.py Fri Aug 08 10:18:10 2008 +0200 +++ b/apps/sort.py Fri Aug 08 10:23:14 2008 +0200 @@ -17,6 +17,27 @@ # You should have received a copy of the GNU Lesser General Public # License along with VIFF. If not, see <http://www.gnu.org/licenses/>. +# This example demonstrates how a secure sorting algorithm can be +# implemented using VIFF. The algorithm used is bitonic sort which was +# chosen in order to maximize the amount of work (comparisons) done in +# parallel. Bitonic sort uses 1/2 * log n * (log n + 1) comparator +# stages and each stage consists of n/2 parallel comparisons. The +# total number of comparisons is thus in O(n log^2 n). +# +# This is larger than the lower bound of O(n log n) for comparison +# based sorting algorithms, achieved by mergesort and other well known +# algorithms. The problem with mergesort is its merging step: to merge +# two sorted arrays of length n/2 one needs up to n comparisons, and +# what is worse, the comparisons must be made one after another. The +# mergesort does one merge with lists of size n/2, two merges with +# lists of size n/4, and so on. This gives a total chain of +# comparisons of length n + n/2 + n/4 + ... + 1 = 2n - 1, which is +# more than the O(log^2 n) stages needed by the Bitonic Sort. +# +# See this page for more analysis and a Java implementation: +# +# http://iti.fh-flensburg.de/lang/algorithmen/sortieren/bitonic/bitonicen.htm + # Give a player configuration file as a command line argument or run # the example with '--help' for help with the command line options.