1. Connection System Serve on mutual connection processors and memory .
University of Technology
Computer engineering and information technology Department
Connection System
Serve on mutual connection processors and memory .
Requirements :
Low latency.
High performance.
Scalability.
Simple implementation.
It possible interconnection change ?
Static(direct) connection only between two nodes.
Dynamic, indirect , change according needed.

2. Connection System It necessary message travel somewhere to deposit?
University of Technology
Computer engineering and information technology Department
Connection System
It necessary message travel somewhere to deposit?
Direct : message go from one node to the second node.
Indirect: message pass multiplexor.
With sharing media, in each time can send out message for one node only.
Routing function:
Permutation ,direct connect each with each.
Broadcast(one for all), multicast (1-M,M-M).
Shift , rotation, shuffle.

3. Interconnection networks
University of Technology
Computer engineering and information technology Department
Interconnection networks
can be classified based on a number of criteria:
Topology (static versus dynamic).
Switching techniques(circuit versus packet).
Control strategy (centralized versus decentralized).
Mode of operation (synchronous versus asynchronous). 3

4. Static (direct connection ) characteristic
University of Technology
Computer engineering and information technology Department
Static (direct connection ) characteristic
It is possible model graph for represent it.
Graph are realize connection each two nodes.
General properties:
Node degree d: count communication links.
Diameter network D: is defined as the maximum shortest paths between any two nodes in the network.
Bisector width B: minimum count links joining tow equal size parts network.
Symmetric: network is same every where.
Homogeneity: all node same.
Latency: time reach other nodes.
Bandwidth: data rate.

5. Static (direct connection ) classification
University of Technology
Computer engineering and information technology Department
Static (direct connection ) classification
1.Completely Connected Networks.
Connection established from any source node to any destination node.
Disadvantage :
Have big number of links.
expensive in terms of the number of links
2. Limited Connection Networks.

6. Linear connection N nodes degree d=2(edge 1), N-1 links.
University of Technology
Computer engineering and information technology Department
Linear connection
N nodes degree d=2(edge 1), N-1 links.
Diameter network D=N-1.
Bisector width B=1.
Nonsymmetrical topology.
Simple realize, non convenient for big N (D~N).

7. Circular connection N nodes degree d=2, N links.
University of Technology
Computer engineering and information technology Department
Circular connection
N nodes degree d=2, N links.
Diameter network D=N/2.
Bisector width B=2 for bidirectional links.
Symmetrical topology.
Create by connect terminal nodes of linear connection.
Decrease diameter.

8. University of Technology
Computer engineering and information technology Department

9. Stare connection N-1 nodes degree d=1 but
University of Technology
Computer engineering and information technology Department
Stare connection
N-1 nodes degree d=1 but
central node degree d=n-1, N-1 links.
Diameter network D=2.
Bisector width B=N/2 links.
nonsymmetrical topology (have a center).
Difficult scalability .
problem for set center.

10. Star connection University of Technology
Computer engineering and information technology Department
Star connection

11. Tree connection Binary tree:N-1 nodes degree d=3, N-1 links.
University of Technology
Computer engineering and information technology Department
Tree connection
Binary tree:N-1 nodes degree d=3, N-1 links.
Diameter network
Bisector width B=1 link.
nonsymmetrical topology.
Good scalability.
Enhance tree ; by nearest from root , where done by add more links.

12. Tree connection University of Technology
Computer engineering and information technology Department
Tree connection

13. Mesh and torus connection
University of Technology
Computer engineering and information technology Department
Mesh and torus connection
Two dimension Grid :N=n² nodes degree d=4.
Diameter network D=2.(n-1)
Bisector width B=n links.
nonsymmetrical topology.
Good scalability.
Torus ; combination grid and circular , half diameter and symmetric topology .

14. Mesh and torus connection
University of Technology
Computer engineering and information technology Department
Mesh and torus connection

15. University of Technology
Computer engineering and information technology Department
Binary hyper cubic
(n) Dimension: the number of directions within a hypercube.
Cubic have :N= , nodes degree d=n.
Diameter network D=n
Bisector width B=N/2 links.
Symmetrical topology.
weak scalability.

16. Binary hyper cubic University of Technology
Computer engineering and information technology Department
Binary hyper cubic

17. University of Technology
Computer engineering and information technology Department

18. University of Technology
Computer engineering and information technology Department
The k-ary n-Cube
(n) Dimension: the number of directions within a hypercube.
(K) Order: the number of nodes along a direction.
Against binary hyper-cubic have along each
(n) dimension (K) nodes (more than 2):
together N= , nodes degree d=2n for tours.
Diameter network D= n.k/2.
Bisector width B= links.
Symmetrical topology.
In general involve : circular, torus, and binary hyper-cubic .

19. The k-ary n-Cube University of Technology
Computer engineering and information technology Department
The k-ary n-Cube