interconnection network
TRANSCRIPT
Cube Interconnection
Networks
Ali Abdul-Zahraa
History
Networking strategy was originally employed in the 1950's by the telephone industry as a means of reducing the time required for a call to go through.
Similarly, the computer industry employs networking strategy to provide fast communication between computer subparts, particularly with regard to parallel machines.
• The performance requirements of many applications, such as weather prediction, signal processing, radar tracking, and image processing, far exceed the capabilities of single-processor architectures.
• Parallel machines break a single problem down into parallel tasks that are performed concurrently, reducing significantly the application processing time.
Why ???
Why???
• Any parallel system that employs more than one processor per application program must be designed to allow its processors to communicate efficiently; otherwise, the advantages of parallel processing may be negated by inefficient communication.
• This fact emphasizes the importance of interconnection networks to overall parallel system performance.
• In many proposed or existing parallel processing architectures, an interconnection network is used to realize transportation of data between processors or between processors and memory modules.
Fundamentals
• In multiprocessor systems, there are multiple processing elements, multiple I/O modules, and multiple memory modules.
• Each processor can access any of the memory modules and any of the I/O units.
• The connectivity between these is performed by interconnection networks.
• In case of multiprocessor systems, the performance will be severely affected in case the data exchange between processors is delayed.
Fundamentals …
• The multiprocessor system has one global shared memory and each processor has a small local memory.
• The processors can access data from memory associated with another processor or from shared memory using an interconnection network.
• Thus, interconnection networks play a central role in determining the overall performance of the multiprocessor systems.
The architecture of a general multiprocessor is shown in Figure 1. In the multiprocessor systems, these are multiple processor modules (each processor module consists of a processing element, small sized local memory and cache memory), shared global memory and shared peripheral devices.
Module communicates with other modules shared memory and peripheral devices using interconnection networks.
NETWORK TOPOLOGYNetwork topology refers to the layouts
of links and switch boxes that establish interconnections.
There are two groups of network topologies: static and dynamic.
Static networks provide fixed connections between nodes. (A node can be a processing unit, a memory module, an I/O module, or any combination thereof.)
With a static network, links between nodes are unchangeable and cannot be easily reconfigured.
Dynamic networks provide reconfigurable connections between nodes.
Static Networks
There are various types of static networks, all of which are characterized by their node degree;
node degree is the number of links (edges) connected to the node.
Some well-known static networks are the following:
Degree 1: shared bus Degree 2: linear array, ring Degree 3: binary tree, fat tree, shuffle-exchange Degree 4: two-dimensional mesh (Illiac, torus) Varying degree: n-cube, n-dimensional mesh, k-ary n-
cube
Diameter
• A measurement unit, called diameter, can be used to compare the relative performance characteristics of different networks.
• More specifically, the diameter of a network is defined as the largest minimum distance between any pair of nodes.
• The minimum distance between a pair of nodes is the minimum number of communication links (hops) that data from one of the nodes must traverse in order to reach the other node.
Cube interconnection network:It is a 3 dimensional interconnection network.
Hyper Cube: A Hypercube interconnection network is an extension of cube network.Hypercube interconnection network for n ≥ 3, can be defined recursively as follows: For n = 3, it cube network in which nodes are assigned number 0, 1, ……,7 in binary. In other words, one of the nodes is assigned a label 000, another one as 001…. and the last node as 111. Then any node can communicate with any other node if their labels differ in exactly one place, e.g., the node with label 101 may communicate directly with 001, 000 and 111. For n > 3, a hypercube can be defined recursively as follows: Take two hypercubes of dimension (n – 1) each having (n –1) bits labels as 00….0, ……11…..1
For n = 4 we draw 4-dimensional hypercube as show in Figure 3
For example, as shown in Figure 4, to route a packet from node 0 to node 5, the packet could go through two different paths, P1 and P2. Here T=000 XOR 101 = 101. If we first consider the bit t0 and then t2, the packet goes through the path P1. Since t0 =1, the packet is sent through the 0th-dimension link to node 1.At node 1, t0 is set to 0; thus T now becomes equal to 100. Now, since t2=1, the packet is sent through the second-dimension link to node 5. If, instead of t0, bit t2 is considered first, the packet goes through P2.
• The cost (complexity) of an n-cube measured in terms of the number of nodes in the cube is O(2^n)
• while the delay (latency) measured in terms of the number of nodes traversed while going from a source node to a destination node is O( log2 N).
• The node degree in an n-cube is O(log2N)
• and the diameter of an n-cube is O(log2N).
FeaturesThe n-cube network has several features that make
it very attractive for parallel computation. It appears the same from every node, and no node needs special treatment. It also provides n disjoint paths between a and a destination.
For example, consider the 3-cube of Figure 2. Since n=3, there are three paths from a source, say 000, to a destination, say 111. The paths are
path 1: 000 001 011 111;path 2: 000 010 110 111;path 3: 000 100 101 111.This ability to have n alternative paths between
any two nodes makes the n-cube network highly reliable if any one (or more) paths become unusable.
Used in some early message passing machines, e.g.:
- Intel iPSC - nCube
RefrencesComputer Architecture" , Mehdi
Zargham, Prentice Hall, 1996