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Static Interconnection Networks
Static Interconnection Networks. CEG 4131 Computer Architecture III Miodrag Bolic. Linear Array. Ring. Ring arranged to use short wires. Linear Arrays and Rings. Linear Array Asymmetric network Degree d=2 Diameter D=N-1 Bisection bandwidth: b=1

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Static Interconnection Networks

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Static Interconnection Networks

CEG 4131 Computer Architecture III

Miodrag Bolic

Linear Array

Ring

Ring arranged to use short wires

Linear Arrays and Rings

Linear Array

Asymmetric network

Degree d=2

Diameter D=N-1

Bisection bandwidth: b=1

Allows for using different sections of the channel by different sources concurrently.

Ring

d=2

D=N-1 for unidirectional ring or for bidirectional ring

Ring

Fully Connected Topology

Needs N(N-1)/2 links to connect N processor nodes.

Example

N=16 -> 136 connections.

N=1,024 -> 524,288 connections

D=1

d=N-1

Chordal ring

Multidimensional Meshes and Tori

Mesh

Popular topology, particularly for SIMD architectures since they match many data parallel applications (eg image processing, weather forecasting).

Illiac IV, Goodyear MPP, CM-2, Intel Paragon

Asymmetric

d= 2k except at boundary nodes.

k-dimensional mesh has N=nk nodes.

Torus

Mesh with looping connections at the boundaries to provide symmetry.

3D Cube

2D Grid

Trees

Diameter and ave distance logarithmic

k-ary tree, height d = logk N

address specified d-vector of radix k coordinates describing path down from root

Fixed degree

Route up to common ancestor and down

Bisection BW?

Trees (cont.)

Fat tree

The channel width increases as we go up

Solves bottleneck problem toward the root

Star

Two level tree with d=N-1, D=2

Centralized supervisor node

Hypercubes

Each PE is connected to (d = log N) other PEs

d = log N

Binary labels of neighbor PEs differ in only one bit

A d-dimensional hypercube can be partitioned into two (d-1)-dimensional hypercubes

The distance between Pi and Pj in a hypercube: the number of bit positions in which i and j differ (ie. the Hamming distance)

Example:

10011 01001 = 11010

Distance between PE11 and PE9 is 3

100

110

000

010

111

101

001

011

0-D

1-D

2-D

3-D

4-D

5-D

*From Parallel Computer Architectures; A Hardware/Software approach, D. E. Culler

Hypercube routing functions

Example

Consider 4D hypercube (n=4)

Source address s = 0110 and destination address d = 1101

Direction bits r = 0110 1101 = 1011

1. Route from 0110 to 0111 because r = 1011

2. Route from 0111 to 0101 because r = 1011

3. Skip dimension 3 because r = 1011

4. Route from 0101 to 1101 because r = 1011

k-ary n-cubes

Rings, meshes, torii and hypercubes are special cases of a general topology called a k-ary n-cube

Has n dimensions with k nodes along each dimension

An n processor ring is a n-ary 1-cube

An nxn mesh is a n-ary 2-cube (without end-around connections)

An n-dimensional hypercube is a 2-ary n-cube

N=kn

Routing distance is minimized for topologies with higher dimension

Cost is lowest for lower dimension. Scalability is also greatest and VLSI layout is easiest.

Cube-connected cycle

d=3

D=2k-1+

Example N=8

We can use the 2CCC network

References

Advanced Computer Architecture and Parallel Processing, by Hesham El-Rewini and Mostafa Abd-El-Barr, John Wiley and Sons, 2005.

Advanced Computer Architecture Parallelism, Scalability, Programmability, by K. Hwang, McGraw-Hill 1993.