Interconnection topologies

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Interconnection topologies

• CS 433
• Laxmikant Kale
• University of Illinois at Urbana-Champaign
• Department of Computer Science

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Distributed memory m/cs
We discussed the communication interface (Ch 7)
PE0
PE1
PEp
Mem0
Mem0
Memp
Interconnection Network
Now, let us talk about the network topology
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Topology requirements

• Must connect each processor to all others
• I.e. it should be possible to send messages
  between any pair of processors
• Desirable
• Intermediate routing, if needed, should happen
  without interfering with computation on
  intermediate nodes.
• Example ring (of theoretical interest only).

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Topology metrics

• What makes one topology better than other?
• What should we measure?
• What can we measure?
• C the number of connections (degree) per node
• How densely is the graph connected?
• Metric Diameter of the graph
• Others?
• How much bandwidth is available?
• Store-and-forward vs. circuit switched
• Number of independent wires
• Bisection bandwidth
• Divide the set of processors in two equal
  partitions
• How much data can flow from one partition to the
  other (per unit time)?
• Take the minimum of this quantity over all
  possible partitionings
• (If all processors were to exchange data with
  random others, ..)

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Ring just to check our definitions

• Let B be the bandwidth of each link
• C2, D P/2, bisection BW 2B
• If every processor wanted to send b bytes to
  every other.

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Grids

• 2D and 3D grids

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Hypercubes

• Definition (recursive)
• To make a hypercube of degree k,
• Take 2 hypercubes of degree (k-1)
• Connect the cooresponding processors from each
  set (with 1 extra link)
• Base case one processor
• Number of processors must be a power of 2
• C log(P)
• Diameter log(P)
• Neighbors?
• Number processors, 0 to P-1, and consider their
  binary representation
• My neighbor in dimension A is obtained by
  flipping my Ath bit.

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K-ary n-cube

• Disadvantage of hypercube?
• Wire lengths? May span the entire machine
• Leads to reduced bandwidth per link
• Number of connections per node increases with the
  size of the machine
• K-ary ncube allows one to seek intermediate
  points between grids and hypercubes.
• N-dimensional hyper cube, but number of
  processors along each dimension is k (instead of
  2 of binary hypercube)

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Writing parallel programs

• Programming model
• How should a programmer view the parallel
  machine?
• Sequential programming von Neumann model
• Parallel programming models
• Shared memory (Shared address space) model
• Message passing model
• Shared Objects model