CSE 291 Interconnection Networks

1. CSE 291 Interconnection Networks Winter 2007 Lecture 6 February 5 2007 Prof. Chung-Kuan Cheng University of California San Diego

2. Circulant Networks • G(n; S) • Example: G(16; 1,4)

3. Circulant Network Properties • 1. k-regular • 2. Strongly connected iff it is connected • 3. Strongly connected iff • 4. Connectivity K(G)=k if G is connected and n is prime • 5. Connectivity K(G)= if G is connected and n is not prime

4. Circulant Networks (cont.) • k-ary n-fly  Butterfly • k-ary n-cube  • 1. n-regular • 2. Connectivity k = n • 3. Diameter n(d-1)

5. Pyramid Networks PN(n) • is adjacent to 4 vertices at level i+1 • Level i is a mesh • Level 0 vertex (1,1,0) is the root

6. … … … … … … Pyramid Network Properties • 1. • 2. • 3. Min degree = 3, max degree = 9 • 4. Diameter 2n

7. Butterfly Networks BN(n) • iff x=y or x differs from y in precisely the (i+1)th bit • level

8. Ω Networks • iff • (1) y is a left cyclic shift of x; or • (2) y is a left cyclic shift of x and then change the last bit • Remark: The routing is identical for all

9. Ω Network is isomorphic to Butterfly Network • Ω(n) BF(n) Left shift & change the last bit Change the (i+1)th bit

10. Shuffle-Exchange Networks SE(n) • and are adjacent iff • (1) x & y differ in precisely the last digit; or • (2) x is a left or right cyclic shift of y • Properties: • (1) • (2) 3-regular • (3) Diameter=2n-1

11. Circuit Switching • Rearrangeable: connect all inputs & outputs when reroute is allowed • Nonblocking in the wide sense: connect all new inputs & outputs if the routing is suitably performed • Nonblocking in the strict sense: connect all new inputs & outputs with no assumptions on the routing