Presenting: Ehud Shavit

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Interconnected NetworksTopologies
The Technion IIT Electrical Engineering
Department 048879 VLSI Architecture Seminar

• Presenting Ehud Shavit

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W.J. Dally
Main Reference
Elsevier, 2004
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Acknowledgements

• Tsutomu Yoshinaga - UEC - Tokyo
• Todd C. Mowry - CMU
• Vincent H. Berk - Dartmouth C.
• Daniel J. Sorin - Duke
• B. Ravikumar - Sonoma S.U.
• William J. Dally - Stanford

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Agenda

• Introduction
• General Properties
• Traffic Patterns
• Terminology
• Performance
• Common Topologies
• Butterfly Topologies
• Torus and Mesh Topologies

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Agenda

• Introduction
• General Properties
• Traffic Patterns
• Terminology
• Performance
• Common Topologies
• Butterfly Topologies
• Torus and Mesh Topologies

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Introduction (1)

• Interconnected NetworkGenerally a Host Area
  Network
• Connecting Processors and memory(and other
  devices)
• May or may not share memory
• Low Latency and High Bandwidth wanted
• The well-known concept closest to NOC

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Introduction (2)

• Parallel Computing Requires FastCommunication
  Between Internal Nodes (Processors and Memories)
• Direct Point-to-Point - O(n2) Wires
• Connections between selected Pairs Routing
  through Intermediate Nodes
• Network Topology Partly Determines Latency and
  Bandwidth

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Introduction (3)

• Applications
• Supercomputers
• Concurrent Computation
• Future of computers inter-device communication

MIT J-Machine (1991)
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Dally is Saying

• We can build networks with 2-4 clocks/hop latency
  (12-24 clocks for a 512-node 3-cube)
• networks faster than main memory access
• need end-to-end hardware support to see this
• Bandwidth of 4GB/s or more per channel (512GB/s
  bisection) is easy to achieve
• nearly flat memory bandwidth
• Topology is a matter of matching pin and
  bisection constraints to the packaging technology
• its hard to beat a 3-D mesh or torus

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Agenda

• Introduction
• General Properties
• Traffic Patterns
• Terminology
• Performance
• Common Topologies
• Butterfly Topologies
• Torus and Mesh Topologies

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General Properties (1)

• Generally Peer-to-Peer Communication
• Single Owner
• Normally 23 212 Nodes
• Nodes are computer devices
• High-end Nodes
• Security - a non-issue

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General Properties (2)

• Generally known Traffic Patterns
• Known and planned Topology
• Every nodes task is normally known
• Resources not low
• Wired and Stationary
• Packaging is a big issue

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Agenda

• Introduction
• General Properties
• Traffic Patterns
• Terminology
• Performance
• Common Topologies
• Butterfly Topologies
• Torus and Mesh Topologies

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Traffic Patterns (1)
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Traffic Patterns (2) Shuffle
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Perfect shuffle s(x)(an-1,an-2,, a1,an)
Inverse perfect shuffle s-1(x)(a1,an
an-1,an-2,, a2)
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Traffic Patterns (3) Butterfly
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butterfly (bit reversal) ß3(x)(a1 , a2 , a3)
?3(x)
2 sub-butterfly ß2(x)(a3, a1, a2)
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Traffic Patterns (4) Shift
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shift a(x) x1 (23)
2 sub-shift a 2(x) x1 (22)floor(x/ 22) 22
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Traffic Patterns (5) Exchange
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E3(x) (a3, a2, a1)
E2(x) (a3, a2, a1)
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Agenda

• Introduction
• General Properties
• Traffic Patterns
• Terminology
• Performance
• Common Topologies
• Butterfly Topologies
• Torus and Mesh Topologies

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Terminology (1)

• Link cable with connectors on each end
• Switch connect k inputs to k outputs
• Phit Minimum of bits physically moved across
  link in one cycle
• Packet Unit that requires routing information,
  some number of Phits
• Topology The mathematical structure of the
  network

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Terminology (2)

• Frequency The rate at which bits are transported
  thru channel c.
• Cut A set of channels, if removed, dividing
  network into two disjoint parts
• Bisection min. number of links that, if removed,
  would separate the network
• Direct All switches attached to host nodes
• Indirect Many switches not attached to host nodes

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Terminology (3)

• Degree outgoing links
• Diameter number of links crossed between nodes
  on maximum shortest path
• Average Hop-Count number of hops to random
  destination
• Critical Length max length of a wire for a
  given nominal frequency

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Terminology (4)

• Channel Load The ratio between the demanded and
  maximum bandwidth
• Channel Width The number of signal running thru
  a channel
• Ideal Throughput the input bandwidth that just
  saturates the bottleneck channel

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Terminology (5)

• Latency The time required for a bit to travel
  thru channel c.
• Average latency without load
• Routers Latency
• Time of Flight
• Serialization Latency

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Terminology (6) - Latency
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Agenda

• Introduction
• General Properties
• Traffic Patterns
• Terminology
• Performance
• Common Topologies
• Butterfly Topologies
• Torus and Mesh Topologies

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Performance

• Degree
• Bisection
• Average Path Hops Count
• Channel Load
• Channel Width
• Ideal Throughput
• Average Latency

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Agenda

• Introduction
• General Properties
• Traffic Patterns
• Terminology
• Performance
• Common Topologies
• Butterfly Topologies
• Torus and Mesh Topologies

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Common Topologies (1)
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Common Topologies (2)
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Agenda

• Introduction
• General Properties
• Traffic Patterns
• Terminology
• Performance
• Common Topologies
• Butterfly Topologies
• Torus and Mesh Topologies

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Butterfly Topology (1)
2-ary 2-fly
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Butterfly Topology (2)

• k-ary n-flies Butterfly Network
• An n stage of radix k switches butterfly network.
  
• Such a network is composed of Nkn
  source/destination terminal nodes
• n stages of kn-1 switching nodes each with k
  inputs and k outputs
• All (n1)N channels are unidirectional.

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Butterfly Topology (3)
2-ary 4-fly
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Butterfly Topology (4)

• All paths equal length
• Unique path from any input to any output
• Conflicts cause tree saturation
• This may be solved using extra stages
• Different forms to do that (After, between)

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Agenda

• Introduction
• General Properties
• Traffic Patterns
• Terminology
• Performance
• Common Topologies
• Butterfly Topologies
• Torus and Mesh Topologies

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Torus/Mesh Topo. (1)
A Simple 8 node ring
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Torus/Mesh Topo. (2)

• k-ary n-cube Torus Network
• An n dimensional of radix k torus network.
• Such a network is composed of Nkn nodes
• n dimensional rings-structure
• k nodes along each ring.
• Each node both a terminal and a switch.
• Bidirectional 2nN channels.

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Torus topology
Torus/Mesh Topo. (3)
2D (4-ary 2-cube)
3D (3-ary 3-cube)
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Torus/Mesh Topo. (4)

• k-ary n-mesh Mesh Networ
• Like a torus but with no ring closing.
• Number of channels

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Mesh topology
Torus/Mesh Topo. (2)
node
2D
3D
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Conclusions

• Interconnected Networks and NOC are close
  relatives
• We should learn and try to duplicate
• Known Topologies
• Known Traffic Patterns
• Known Routing Protocols
• etc...

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Networks MeshButterflies
KarlFriedrich Hieronymus Baron of Munchausen
(1720-1797)