Polytechnic Institute of NYU
Page 2
of
18
CS6143
Handout No : 7
October 20, 2010
A1)
The 3-CCC has 24 nodes.
Each node has a unique address : (i, j) where “j” indicates which corner of
the 3-CCC the node resides at and “i” indicates which node of the corner.
To form a 3-CCC, we connect node (i,j) to node (i,m) if and only if “m” is the result of inverting the “i”
th
bit (from
left, starting at 1) of the binary representation of “j.”
For example, for node (1,3), the connection to the next corner is
to node (1,7).
Because, “i” is 1 and “j” is 3 (or 011).
“m” is 7 (111) since we invert bit one from left of “j.”
Below is
the 3-CCC with the ring embedded :
The ring includes all the nodes of the 3-CCC and can be traversed in many ways : with different starting points and
different paths.
All of these long rings have the same length : 24 links.
This ring is shown by thick lines in the above
picture.
Here is one ring starting at (2,1) :
(2,1)-(2,3)-(1,3)-(3,3)-(3,2)-(2,2)-(1,2)-(1,6)-(2,6)-(3,6)-(3,7)-(1,7)-(2,7)-(2,5)-(1,5)-(3,5)-(3,4)-(2,4)-(1,4)-(1,0)-
(2,0)-(3,0)-(3,1)-(1,1)-(2,1).
Q2)
Consider the following static direct
interconnection network :
(3,1)
(2,1)
(1,1)
(3,0)
(1,0)
(2,0)
(1,4)
(2,4)
(3,4)
(2,2)
(1,2)
(3,2)
(3,5)
(2,5)
(1,5)
(2,6)
(1,6)
(3,6)
(3,7)
(2,7)
(1,7)
(3,3)
(2,3)
(1,3)
starting
point
Apex
Level 2
Level 1
Level 0
Base
This is a pyramid network of size k
2
or size 16.
Make observations on the network, including
(i) the number of nodes,
(ii) the degree,
(iii) the diameter
and
others
as a function of
k
based on the discus-
sion of interconnection networks in class.
Note that in the pyramid network, all, except base
nodes, have four children each, on the level below.