1 / 12

Static Interconnection Networks - PowerPoint PPT Presentation

Static Interconnection Networks. 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

Related searches for Static Interconnection Networks

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about 'Static Interconnection Networks' - elle

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Static Interconnection Networks

Miodrag Bolic

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

• 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

• 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

• 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?

• 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

• 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

• Example

Consider 4D hypercube (n=4)

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

• 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.

• d=3

• D=2k-1+

• Example N=8

• We can use the 2CCC network

• 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.