This preview shows page 1. Sign up to view the full content.
Unformatted text preview: he values in every ÝÞ plane, alternating the order between planes (a ÝÞ plane is the set of processors with
µ½
Æ½
Æ ).
ﬁxed Ü, ´Ü
4.Do two steps of the 1dimensional oddeven sort on each Ürow (an Ürow is the set of processors with ﬁxed Ý
and Þ , ´ Ý Þ µ ½
Æ ).
5.Sort the values in every ÝÞ plane.
For each of the plane sorts in steps 1, 2, 3, and 5, we use the Æ ¢ Æ sort we discussed in class, which takes ¢´Æ µ
time. Step 4 only takes 2 time, so we have a total running time of ¢´Æ µ.
Now we need to argue correctness a bit. 1 We consider only 01 inputs as per the 01 lemma. After step 1, on each
ÜÞ plane, the ¼’s are moved towards the smallest value of Ü. Since the values are sorted, there can be at most one
dirty Þ column in each plane. Thus, every Ücolumn within a single ÜÞ plane has (almost) the same number of ¼’s (to
within one).
In step 2, we sort ÜÝ planes. Thus, we pull one Ücolumn from each of the ÜÞ planes. Since each of the Ücolumns
in a given ÜÞ plane has within one the same number of ¼’s, the ÜÝ planes differ by at most Æ ¼’s. Thus, after we sort
the values in each ÜÝ plane, almost all the ÝÞ planes are clean. In fact, we can only have two adjacent dirty ÝÞ planes.
More speciﬁcally, all the ÝÞ pla...
View
Full
Document
This document was uploaded on 03/20/2014 for the course EECS 6.896 at MIT.
 Spring '07
 BradleyKuszmaul

Click to edit the document details