COMP5426 Distributed

Parallel A

Interconnects are links (wires, fiber).

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Interconnection networks carry data between processors and to memory.

Static networks consist of point-to-point communication links among processing nodes

so referred to

Dynamic networks are built using switches

of switches an

munication links. Dynamic networks

referred to as indirect networks.

ct networks.

ne is designed

Static networks form all connections when

the connection is needed. In a static network, messages must be routed alon

links. This

message must hop through intermediate

Dynamic networks establish

en two or more nodes

messages are routed along t

r than when

eans a single

destination.

a connection

on the fly as

Topologies

iety of network

been proposed and implemented.

These topol

ogies trade

performance for cost and scalability.

Commercial machines often impleme hybrids of multiple topologies for

asons of pa

ailable components.

topologies have

Static Network Topologies:

essor is conn

The number of links in the network

scales as O(p2).

ile the performance scales very

hardware complexity is n

values of p.

Static Network Topologies:

Every node

the center.

Distance between any pair However, the central node

only to a c

ommon node at

of nodes is O(1). becomes a bottleneck.

Static Network

A further generalization t nodes with 2d neighbors.

A special case of a d-dimensio hypercube. Here, d = log p, wh

Topologies:

eshes, and

In a linear array, each node has two neighbors, one to its left and one to its right. If the nodes at either end are connected, we

A generalization to 2 dimensions has nodes with 4 neighbors, to the north, south, east,

nal mesh ere p is t

Static Network

Topologies:

Linear arrays: (a) with

no wraparound

links; (b)

aparound link.

Network Topologies:

Two and three dimensional meshes: (a) with no wraparound; (b) 2-D mesh with link (2-D torus); and (c) a 3-D mesh wit

2-D mesh wraparound

Static Network Topologies:

their Constru

Static Network Topologies:

Properties

most log p.

log p neighbors.

The distance between any two n

The distance between two nodes is

given by th

at which the

two nodes differ.

Static Network Topologies:

Dynamic Network Top

Links higher up the

more traffic than t

The distance between any two

For this reason, a variant called a fat-tree,

rossings. rees.

can be laid out in 2D with no wire

tree potentially carry

the lower leve

an attractive property of

Dynamic Network

All processors ac exchanging data.

However, the bandwidth is a major bottleneck.

Typical bus

dozens of nodes.

ed machine

cess a common

The distance between any two node O(1) in a bus. The bus also provides convenient broadcast media.

Dynamic Network

Dynamic Network

grows as O(p2).

is generally diffic

values of p.

crossbar o

Dynamic Network

Multistage

Multistage inte

compromise between

poor performance scalability.

excellent performanc

ility, but poor cost scalability.

ects strike

scalability,

these extremes.

Dynamic Network

Multistage

Dynamic Network

the most commonly

s network cons

interconne

where p is the number of inputs/outputs.

f log p stages,

Dynamic Network

Dynamic Network

The perfect shu connected using

ffle patterns are p/2 2×2 switches.

he 2×2 switches operate in two mod pass-through or crossover.

Dynamic Network

An omega networ

k has p/2 × log p switching nodes,

h a network grow

O(p log p).

Multistage

Let s be the binary r

p switching Note that t

ce and d be that

The data traverses the link switching node. If the most

routed in pass-through mode by the switch else, it switches to crossover.

stages. his is not

epresentation of the

non-blocking

to the first significant bits

Multistage

Evaluating In

Diameter: The distance betwe

two nodes in the network. The diameter of

ear array is p −

1, that of

at of a tree and hypercube is log p, and t

completely connected network is O(1).

Arc Connectivity: the minimum number of a that must be removed from the network to break it into two disconnected network.

Bisection Width:

must be cut to

equal parts. The bisection width of a linear

array and tree is 1, that of a mesh is

of a hypercube is p/2 and that of a completely connected network is p2/4.

a mesh is 2(

mum number

Evaluating In

network, the lengt

Cost: The number of links or switches

(whichever

symptotically higher) is

a meaningful measure of the cost. However, a number of other factors,

h of wires, etc., also

Evaluating In

Evaluating In

The total time to tran a network comprises o

programming r

Startup time (ts): Time spent at sending receiving nodes (executing the routing

algorithm,

time (th): This

number of hops and includes factors such as

switch latencies, network delays, etc.

Per-word transfer time (tw): This time incl all overheads that are determined by the l

of the message. This includes bandwidth of

links, error checking

sfer a message over f the following:

function of

ection, etc.

Simplified

we can approximat

transfer by

cally smaller

cost of message

ication Costs in

It is important to note that the original expression for communication time is valid for only uncongested networks

The actual cost of communication is dependent on a variety of features including the programming model semantics, the network topology, dat handling and routing, and associated software protocols

Parallel Machines

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