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Parallel Processingsp2016

lec#8

Dr M Shamim Baig 

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Interconnection Networks (INs)

for Parallel Computers

1.2

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Static INs:

 Evaluation Parameters• Degree : Max of links connected

at any node of the netork

• Diameter : !istance "shortest path$eteen the farthest nodes in the

netork.

• Link Cost : %otal &'($er of links

re)'ired to i(ple(ent the netork.

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1.*

Static INs: Topologies

• +o(pletely +onnected

• ,tar 

• %ree• -inear rray / ing

• 2! 3! Mesh / %or's

• yperc'$e

• kd Mesh

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,tatic 5&s topologies: +o(pletely +onnected

"a co(pletelyconnected netork of eight nodes"$ a star connected netork of nine nodes.

• 7ach processor is connected toeery other processor9"number

of processors= p

• !ia(eter19 n'($er of links in

the netork are p (p-1) / 2 

• ;hile perfor(ance scales ery

ell9 hardare co(plexity is not

reali

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• %ree is a graph itho't any loops.?ood for hierarchical co(( (odel• %ree inoles root9 leaes9 parent9

child9 leels9 height• 5n +o(plete $inary tree each node

has 3neigh$ors "degree391parent / 2children "except root hasno parent / leaes hae no child

•   pnode co(plete $inary tree has2i nodes at ith leel / log"p@1 leels(root level is )

• %ree has link cost p1• %ree has !ia(eter 2

• %rees can $e laid o't in 2! ith no

ire crossings9 ease of (an'fact're.

,tatic 5&s topologies: %ree

log"p@1 1

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,tatic 5&s topologies:

>attree

  "a +o(plete $inary tree 5& "$ >attree 5&

• -inks higher 'p thetree potentially

carry (ore traffic

than those at the

loer leels.

• >or this reason9 a

ariant called a fat

tree9 fattens thelinks as e go 'p

the tree.

• Pop'lar topology

for !ata +enters

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,tatic 5&s topologies:

 -inear rray ing

-inear arrays: "a ith no raparo'nd links

"$ ith raparo'nd link "ring

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,tatic 5&s topologies:

 -inear rray / ing

• 5n a linear array9 each node has to neigh$ors9one to its left / one to its right"except endnodeshich hae one neigh$or 

• 5n an array9 een if a single nodelink fails array

partitions in to parts.• 5f array nodes at either end are connectedtogether9 it $eco(es a ring "in hich all nodesare identically connected to to neigh$ors

• 5n a ring9 if a single nodelink fails9 re(ainingnodes are still connected as an array.

• 5n an array each pair of nodes has only one pathhile in ring they hae to alternate paths

• ing is sy((etrical / has $etter red'ndancy

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,tatic 5&s topologies:

 -inear rray / ing

•   pnode -inear array has: B !egree 2

 B !ia(eter p1 B -ink cost p1

•   pnode ing has:

 B !egree 2 B !ia(eter floorCp2D B -ink cost p

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,tatic 5&s topologies:

2! Mesh %or's

2-imensional !es":

 (a) 2- mes" wit" no wraparoun# ($) 2- mes" wit" wraparoun# link (torus)

• 5n 2di(ension (esheach node has *neigh$ors each to thenorth9 so'th9 east9 /est "except the edge

nodes •   2! (esh ith

rapped aro'nd linksat corresponding edgenodes in each 

di(ension is a %or's. 5n tor's9 all nodes areidentically connectedto *neigh$ors

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Static INs topologies:

 2- !es"%Torus

•   pnode 2! s)'are Mesh" x has: B !egree *

 B !ia(eter 2" 1 B -ink cost "2p B 2 2"p

•   pnode 2! s)'are %or's" x has: B !egree * B !ia(eter 2 x floorC 2D B -ink cost 2p

o a$o't nons)'are "( x n Mesh / tor'sEEE

,t ti 5& t l i $

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,tatic 5&s topologies: yperc'$es

+onstr'ction of hyperc'$es fro( hyperc'$es of loer di(ension.

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,tatic 5&s 7al'ation:

2!9 3!9 G..k! Mesh

2-imensional !es":

 (a) 2- mes" wit" no wraparoun# ($) 2- mes" wit" wraparoun# link(c) &- mes" no wrap aroun#

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Static INs Evaluation: k-d  !es"

• Mesh%or's can $e generali

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k-d  !es": Evaluation parameters

•   "sy((etric kd (esh has knodes in each of ddi(ensions   p= & !  no!es•  ' (smmetric) &-! mesh ( +ith +rap aroun!) has:- BDegree= 2!  BDiameter= ! * floor,&/2  B.in& cost= ((2!) * p) / 2 = ! * p

• o+ about evaluation parameters of (smmetric) &-! mesh

( +ithout +rap aroun!)

•  ' ( non-smmetric  ) &-! mesh has k i  no!es in d i  !imensionan! therefore +ill have !ifferent formulae to compute theevaluation parameters

, f 7 l ti P t

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,'((ary of 7al'ation Para(eters:

,tatic 5nterconnection &etorks

Network  iameter

Hisection

;idth

'ink-cost

(no% of lin&s)

Completel-connecte#

Star

Complete $inar tree

'inear arra 

2- mes" no +raparoun!  2- mes" +raparoun! 

*percu$e

k-# mes" raparo'nd

 

!egree

p1

p1

3

2

*

*logp

+ing

2d