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CSE 8383 - Advanced Computer Architecture

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Path, path length, shortest path. Cycles, cyclic vs. acyclic ... Delay: latency. Blocking characteristics. Fault tolerance. Switch Modules. A x B switch module ... – PowerPoint PPT presentation

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Title: CSE 8383 - Advanced Computer Architecture


1
CSE 8383 - Advanced Computer Architecture
  • Week-11
  • April 1, 2004
  • engr.smu.edu/rewini/8383

2
Contents
  • Message Passing (Distributed Memory) Systems
  • Static Networks
  • Dynamic Networks

3
MIMD Distributed Memory Systems
P
P
P
P
Interconnection Networks
4
Distributed Memory
  • Multiple address spaces
  • Communication via send receive
  • Synchronization via message passing

5
Interconnection Network
  • Several IN classification criteria
  • Mode of operation synchronous vs. Asynchronous
  • Control strategy centralized vs. decentralized
  • Switching techniques circuit vs. packet
    switching
  • Topology static vs. dynamic

6
Interconnection Network Taxonomy
Interconnection Network
Dynamic
Static
Bus-based
Switch-based
1-D
2-D
HC
Crossbar
Single
Multiple
SS
MS
7
Static Interconnection Networks
  • Direct links, which are fixed once built
  • Fixed Connections, unidirectional or
    bi-directional
  • Fully Connected (Completely Connected Network
    (CCN))
  • Limited Connection Network (LCN).

8
Dynamic Interconnection Networks
  • Communication patterns are based on program
    demands
  • Connections are established on the fly during
    program execution
  • Multistage Interconnection Network (MIN) and
    Crossbar

9
Static Network Topology
  • Linear arrays
  • Ring (Loop) networks
  • Two-dimensional arrays
  • Tree networks
  • Cube network
  • .

10
Static Network Analysis
  • Graph Representation
  • Parameters
  • Cost
  • Degree
  • Diameter
  • Fault tolerance

11
Graph Review
  • G (V,E) -- V nodes, E edges
  • Directed vs. Undirected
  • Weighted Graphs
  • Path, path length, shortest path
  • Cycles, cyclic vs. acyclic
  • Connectivity connected, weakly connected,
    strongly connected, fully connected

12
Linear Array
N nodes, N-1 edges
Node Degree
Diameter
Cost
Fault Tolerance
13
Ring
N nodes, N edges
Node Degree
Diameter
Cost
Fault Tolerance
14
Chordal Ring
N nodes, N edges
Node Degree
Diameter
Cost
Fault Tolerance
15
Barrwl Shifter
  • Number of nodes N 2n
  • Start with a ring
  • Add extra edges from each node to those nodes
    having power of 2 distance
  • i j are connected if j-I 2r, r 0, 1, 2,
    , n-1

16
Barrel Shifter N 16
Node Degree
Diameter
Cost
Fault Tolerance
17
Tree and Star
Node Degree
Diameter
Cost
Fault Tolerance
18
Mesh and Torus
N nn
Node Degree Internal ? 4 Other ? 3, 2
Diameter 2(n-1)
Node Degree 4
Diameter 2 floor(n/2)
19
Fully Connected
Node Degree
Diameter
Cost
Fault Tolerance
20
Hypercubes
  • N 2d
  • d dimensions (d log N)
  • A cube with d dimensions is made out of 2 cubes
    of dimension d-1
  • Symmetric
  • Degree, Diameter, Cost, Fault tolerance
  • Node labeling number of bits

21
Hypercubes
0
1
d 0
d 1
d 2
d 3
22
Hypercubes
23
Hypercube of dimension d
N 2d
d log n
Node degree d
Number of bits to label a node d
Diameter d
Number of edges nd/2
Hamming distance!
Routing
24
Subcubes and Cube Fragmentation
  • What is a subcube?
  • Shared Environment
  • Fragmentation Problem
  • Is it Similar to something you know?

25
Cube Connected Cycles (CCC)
  • k-cube ? 2k nodes
  • k-CCC from k-cube, replace each vertex of the k
    cube with a ring of k nodes
  • K-CCC ? k 2k nodes
  • Degree, diameter ? 3, 2k
  • Try it for 3-cube

26
K-ary n-Cube
  • n cube dimension
  • K nodes along each dimension
  • N kn
  • Wraparound
  • Hupercube ? binary n-cube
  • Tours ? k-ary 2-cube

27
Analysis and performance metrics static networks
  • Performance characteristics of static networks

Network Degree(d) Diameter(D) Cost(link) Symmetry Worst delay
Fully connected N-1 1 N(N-1)/2 Yes 1
Linear Array 2 N-1 N-1 No N
Binary Tree 3 2(?log2N? 1) N-1 No log2N
n-cube log2N log2N nN/2 Yes log2N
2D-Mesh 4 2(n-1) 2(N-n) No ?N
K-ary n-cube 2n n?k/2? nN Yes K x log2N
28
Dynamic Network Analysis
  • Parameters
  • Cost number of switches
  • Delay latency
  • Blocking characteristics
  • Fault tolerance

29
Switch Modules
  • A x B switch module
  • A inputs and B outputs
  • In practice, A B power of 2
  • Each input is connected to one or more outputs
    (conflicts must be avoided)
  • One-to-one (permutation) and one-to-many are
    allowed

30
Binary Switch
Legitimate States 4
Permutation Connections 2
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