MESSAGE ROUTING SCHEMES IN A HYPERCUBE MACHINE

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MESSAGE ROUTING SCHEMES IN A HYPERCUBE MACHINE

• S. Raghupathy,
• M. R. Leuze, and
• S. R. Schach
• Presented by Syed Md. Shakir

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What are Interconnected Networks and why do we
need them?

• One way for processors to communicate data is to
  use a shared memory and shared variables. However
  this is unrealistic for large numbers of
  processors. A more realistic assumption is that
  each processor has its own private memory and
  data communication takes place using message
  passing via an Interconnection Network.
• The interconnection network plays a central role
  in determining the overall performance of a
  multicomputer system. If the network cannot
  provide adequate performance, for a particular
  application, nodes will frequently be forced to
  wait for data to arrive.

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Parallel Computers

• Large-scale parallel computers are potential
  candidates for providing very high computational
  power
• These systems are usually organized as an
  ensemble of nodes, each with its own processor,
• local memory, and other supporting devices.
• The nodes are interconnected using a variety of
  topologies that can be classified into two broad
  categories
• Direct
• Indirect.

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Direct Networks

• In direct networks, each node has a
  point-to-point or direct connection to some of
  the other nodes, called neighboring nodes
• examples of direct network topologies include
  hypercube, mesh, and tree.

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Indirect Networks

• In indirect networks, the nodes are connected to
  other nodes or a shared memory through one or
  more switching elements.
• Examples of indirect networks include crossbar,
  bus, and multistage interconnection networks.

Multistage interconnected Network
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Indirect Network

Cross Bar
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Communication Latency

• The communication latency of direct networks
  depends on several factors including switching,
  routing, flow control, and topology. Several
  switching techniques have been proposed for
  direct networks.
• Wormhole switching has emerged as a popular
  technique and has been used in both commercial
  and experimental systems.
• Wormhole switching can be employed in both direct
  and indirect networks. It is widely used in
  contemporary multicomputer because of its low
  latency and requirement of small buffers at the
  nodes.

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cont...

• The mesh is an asymmetrical topology in which the
  node degree depends on its location.
• Interprocessor communication performance depends
  on the location of source and destination.
• The torus and hypercube are symmetrical
  topologies in which the degree of a node is the
  same irrespective of its location in the network.
  Thus, unlike the mesh, all the nodes in tori and
  hypercubes are identical in connectivity.

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Routing in Parallel Computers

• Parallel computers are modeled by directed graphs
• All interconnections between processors (nodes)
  occur in synchronous steps
• Each link can carry at most one unit message
  (packet) in one step
• During a step, a node can send at most one packet
  to each of its neighbors
• Each node is uniquely identified by a number
  between 1 and N

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Switching Techniques

• In most multicomputer systems, a message enters
  the network from a source node and is switched or
  routed towards its destination through a series
  of intermediate nodes.
• Four types of switching techniques are usually
  used for this purpose
• circuit switching
• packet switching
• virtual cut-through switching
• wormhole switching.

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Circuit Switching

• In circuit switching, a dedicated path is
  established between the source and the
  destination before data transfer initiates.
• Once the data transfer is initiated the message
  is never blocked.
• As the channels creating the path are reserved
  exclusively, buffering of data is not required.
• On the other hand, establishing the path requires
  significant overhead during the
  data-transmission
• phase, all channels are reserved for the entire
  duration of message transfer.
• Circuit switching thus degrades performance and
  is no longer used in commercial multicomputer
  systems.

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Packet Switching

• In packet switching, a message is divided into
  packets that are independently routed towards its
  destination.
• The destination address is encoded in the header
  of each packet. The entire packet is stored at
  every intermediate node and then forwarded to the
  next node in its path.
• The main advantage of packet switching is that
  the channel resource is occupied only when a
  packet is actually transferred.

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Packet Switching cont...

• Each packet contains the routing information and
  alternative paths can be selected upon
  encountering network congestion or faulty nodes.
• The major drawback of packet switching
• Since the packet is stored entirely at each
  intermediate node, the time to transmit a packet
  from source to destination is directly
  proportional to the number of hops in the path.
• At each intermediate node, we need buffer space
  to hold at least one packet.

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Virtual Cut Through

• In order to reduce the time to store the packets
  at each node, Kermani and Kleinrock introduced a
  technique called virtual cut-through
• In this, while routing toward its destination, a
  message is stored at an intermediate node only if
  the next channel required is occupied by another
  packet.
• Now, the distance between the source and
  destination has little effect on communication
  latency.

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cont...

• In an extreme case, when a message encounters
  blocking at all the intermediate nodes, the
  virtual cut-through technique reduces to packet
  switching.
• The disadvantage of the virtual cut-through
  technique
• Implementation cost each node must provide
  sufficient buffer space for all the messages
  passing through it, and because multiple messages
  may be blocked at any node, a very large buffer
  space is required at each node.
• This implementation constraint limits the use of
  virtual cut-through technique.

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Wormhole Switching

• Wormhole switching is a variant of the virtual
  cut-through technique that avoids the need for
  large buffer spaces.
• In wormhole switching, a packet is transmitted
  between the nodes in units of flits, the smallest
  units of a message on which flow control can be
  performed.
• The header flit(s) of a message contains all the
  necessary routing information and all the other
  flits contain the data elements.
• The flits of the message are transmitted through
  the network in a pipelined fashion.

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cont...

• Since only the header flit(s) has the routing
  information, all the trailing flits follow the
  header flit(s) contiguously.
• Flits of two different messages cannot be
  interleaved at any intermediate node.
• Successive flits in a packet are pipelined
  asynchronously in hardware using a handshaking
  protocol.
• When the header flit is blocked, then all the
  trailing flits occupy the buffers at the
  intermediate nodes.

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Wormhole Switching
Messages

D
H
Packets
Flits
D
D
D
D
D
D
D
D
D
D
D
D
D
D
H
D Data Flit H Header Flit (a)
(b)
Message format and routing in Wormhole Switching
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Advantages of Wormhole Switching

• The main advantage of wormhole switching derives
  from the pipelined message flow since
  transmission latency is insensitive to the
  distance between the source and destination.
• Moreover, since the message moves flit by flit
  across the network, each node needs to store only
  one flit.
• Some implementations, however, require storage of
  multiple flits at each node to improve routing
  performance. The reduction of buffer
  requirements at each node has a major effect on
  the cost and size of multicomputer systems.

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Disadvantages of Wormhole Switching

• The main disadvantage of wormhole switching comes
  from the fact that only the header flit has the
  routing information.
• If the header flit cannot advance in the network
  due to resource contention, all the trailing
  flits are also blocked along the path and these
  blocked messages can block other messages.
• This chained blocking can also lead to deadlock
  where messages wait for each other in a cycle and
  hence no message can advance any further.

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cont...

• Prevention of deadlock is one of the main issues
  in wormhole switching, and is usually
  accomplished by a suitable choice of routing
  function that selectively prohibits messages from
  taking all the available paths, thus preventing
  cycles in the network.
• Selection of a routing algorithm is thus a major
  issue in wormhole-switched networks.

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Hypercube Network

• An n-dimensional hypercube network
• Number of nodes N 2n
• Degree n
• The node i with address (i1, i2, , in) ? 0, 1n
  and the node j with address (j1, j2, , jn) ? 0,
  1n are connected if the hamming distance between
  (i1, i2, , in) and (j1, j2, , jn) is 1

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Hypercube Topology
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4d Hypercube

• K dimensional hypercube is formed by combining
  two k-1 dimensional hypercubes and connecting
  corresponding nodes i.e. hypercubes are
  recursive, each node is connected to k other
  nodes i.e. each is of degree k.

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Static routing in Hypercube

• Given a source node Ns
• Destination node Nd
• The addresses of the 2n processors can be
  represented using n bits.
• Then the next node on the route
• from Ns to Nd is the node represented by bit
• pattern (en-l, . . ., cl, CO) with bit i
  flipped, that
• is to say, the message is routed in dimension
  i
• The algorithm continues in this way until
• the message arrives at node Nd.

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Static routing

• Algorithm
• Given a destination address d(i) and an
  intermediate node ?(i)
• Compare the bits of d(i) with ?(i) from left to
  right
• Identify the first bit position at which these
  two addresses differ
• Route this packet to its neighbor n(i) such that
  ?(i) and n(i) differ only in this bit position

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Static Routing Algorithm

• Example
• Source (0, 0, 0, 0, 0, 0)
• Destination (1, 0, 1, 0, 1, 1)
• (0, 0, 0, 0, 0, 0) ? (1, 0, 0, 0, 0, 0) ?
• (1, 0, 1, 0, 0, 0) ? (1, 0, 1, 0, 1, 0) ?
• (1, 0, 1, 0, 1, 1)

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Advantages and Disadvantages

• Advantage
• No overhead for calculating new routes.
• Same CPU cycles can be used for other
  computational purpose.
• Disadvantage
• Blocking is a common consequence.

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Dynamic routing

• It allows every message to select the (locally)
  optimal route under the current circumstances.
• In Dynamic routing, if link is blocked then
  attempt is made to pass the message through other
  link.
• More utilization of the network
• It uses local knowledge.

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Dynamic routing

• Allows the message to route from Ns,
• to Nd ,depending on circumstances.
• Allows optimal route under the current
  circumstances
• Overhead of implementing dynamic routing.
• At each node calculations have to be performed to
  determine the next node to which the message
  should be routed,
• and links have to be tested to see which ones
  are free.

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Advantages And Disadvantages

• Advantages
• Blocking is not a major problem
• Disadvantages
• overhead of implementing dynamic routing.
• At each node calculations have to be performed to
  determine the next node to which the message
  should be routed,
• links have to be tested to see which ones
• are free.
• The size of the overhead will vary
• from hypercube to hypercube. In some
• machines, the additional work can be done in
• hardware in parallel with other operations in
• other machines, it must be done in software,
• using machine cycles that could otherwise be
  used for productive computing.

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PRIORITIZATION

• If a number of messages are waiting to use a
• link, one method of choosing which message
• to transmit is on the basis of
• (FIFO), the method used in commercial
• hypercubes.
• In the paper alternative prioritization schemes,
  such as LIFO, giving priority to the message with
  the maximum number of remaining hops is also
  considered

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Other Prioritization Schema

• The processes form a DAG, each process can be
  assigned a sequence number such that every
  message is sent to a process with a higher
  sequence number than the sequence number of the
  process that generated the message.
• The sequence number of the generating process can
  then be used to prioritize messages

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Message Format
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The Prioritization Schema
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The Simulator

• The simulator was constructed to investigate
  routing strategies.
• The header contains information such as source
  and destination node, as well as information
  needed when the order of transmission of messages
  is done on the basis of
• prioritization, such as sequence number, time
  generated, arrival time at the current node, and
  number of hops that still have to be traversed.

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Execution Cycle Of The Simulator

• The simulator has three phases
• Message generation
• Message ordering
• Message routing.

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Message Generation Phase

• In this phase each active process is checked to
  see if it has received all the messages it
  requires.
• If so, the messages it is to transmit are
  generated, and placed in the message buffer.
• The process then terminates.
• After all possible messages have been
• generated, the simulator enters the message
  ordering phase.

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Message Ordering Phase

• After entering the message ordering phase the
  messages in each buffer are ordered according to
  the prioritization scheme currently being
  evaluated.
• In the case of equal priorities, ties are broken
• randomly.
• Finally, the message routing cycle commences.

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Message Routing Phase

• After each message is fetched from the message
  buffer and an attempt is made to transmit it to a
  neighboring node.
• If static routing is being used, and the
  predetermined link is in use, then that
  particular message is blocked.
• When dynamic routing is used, an attempt is made
  to transmit the message over the first unused
  link that will move it closer to its destination.

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Results

• Dynamic routing performs better than static
  routing, but the improvement factor varies
  depending on the prioritization scheme. At best,
  the improvement is by a
• factor of two.
• Best results occur when priority is given to
  messages with the lowest sequence number.
• Results almost as good are obtained when priority
  is given to messages with the fewer number of
  hops, either in the original message or remaining
  to be traversed.

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Results Continued...

• Messages of lowest sequence number are
  essentially those transmitted earliest in the
  computation sequence. Giving priority to such
  messages essentially speeds up the rate at which
  processes can begin transmitting, and hence
  speeds up the computation as a whole.
• The traffic congestion in the hypercube is
  decreased by giving priority to messages with the
  fewest numbers of hops and therefore allowing the
  longer messages to proceed with less blocking
  than would otherwise be the case.
• By giving priority to messages with fewer
  choices, the
• overall amount of blocking is decreased

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One Bidirectional Link Between Nodes
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Two Unidirectional Links Between Nodes
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Percentage Improvement When Two Unidirectional
Lines Are Used
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Observations From The Graphs Above

• Having two unidirectional links improve
  throughput over one bidirectional link
• Note Improvement depends on the prioritization
  scheme.
• The percentage improvement is rarely more than
  fifteen per cent, and is usually much smaller.
• This effect may be caused by the fact that the
  problem graph is a DAG, thereby imposing a
  directionality on the flow of messages

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Conclusions

• Throughput of a certain class of problems on a
  hypercube can be increased by up an order of two
  through use of dynamic rather than static routing
  algorithms, and also by prioritizing the
  messages.
• It is likely that different prioritization
  schemes would yield
• improved throughput for other classes of
  problems.

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Questions ?