ceg4131 static networks

8/2/2019 Ceg4131 Static Networks

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Static Interconnection Networks

CEG 4131 Computer Architecture III

Miodrag Bolic


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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 sourcesconcurrently.

Ring

d=2

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

Linear Array

Ring

Ring arranged to use short wires

2/ND


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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 Example

N=16, d=3 -> D=5


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Multidimensional Meshes and Tori

Mesh

Popular topology, particularly for SIMD architectures since they match manydata 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.

2D Grid 3D Cube


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Trees

Diameter and ave distance logarithmic

k-ary tree, height d = logk N

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

Fixed degree

Route up to common ancestor and down Bisection BW?


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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


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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)-dimensionalhypercubes

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

Example:

10011 01001 = 11010

Distance between PE11 and PE9 is 3

0-D 1-D 2-D 3-D 4-D 5-D

001 011

000 010

100 110

111101

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


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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 = 10113. Skip dimension 3 because r = 1011

4. Route from 0101 to 1101 because r = 1011


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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 higherdimension

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


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Cube-connected cycle

d=3

D=2k-1+

Example N=8

We can use the 2CCC network

2/k


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References

1. Advanced Computer Architecture and Parallel

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

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

1993.
http://ca.wiley.com/WileyCDA/WileyTitle/productCd-0471467405.htmlhttp://ca.wiley.com/WileyCDA/WileyTitle/productCd-0471467405.html

ceg4131 static networks

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