Parallel Computing using Linux Clusters

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Parallel Computing using Linux Clusters

• PFract A Parallelized Fractal Generation Program

Srivas N. Chennu Vishwas N. 8th Semester
CSE R.V.C.E Bangalore
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The Linux Cluster

• Collection of computing nodes.
• Interconnected by a high-speed network
  architecture.
• Nodes are conventional PCs running the Linux OS.
• Master Slave Design.
• Highly scalable.
• Extensive use in large-scale parallel computing.

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The PFract System

• Parallelized Fractal Generator for Mandelbrot and
  Julia images.
• Used as an example system to explain the
  parallelization process.
• Splits up the computation into smaller segments.
• Executes parallelized segments in concurrently on
  a cluster.

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The Fractal

• Mathematical shape of fractional dimensions.
• Self-similarity at every level of scaling.
• Iterative feedback equation.
• Number of iterations determines image depth and
  clarity.
• Ideal candidate for parallelization.
• Inherent parallelism.
• Processor intensive.

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The Fractal Algorithm

• The sequential algorithm for the Mandelbrot Set.
• Initialize 2-D fractal plane of X iY.
• Consider a point (X,Y). Initialize C X iY.
• Iteratively compute feedback equation.
• Zn 1 Zn2 C where Z0 0.

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Continued

• If Z -gt Infinity then X iY does not belong the
  fractal set.
• If value of Z converges to a finite set of points
  then it belongs to the set.
• Mark point in fractal plane using a color-coding
  scheme.
• Repeat above steps for every point.

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The Parallelization Process
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Decomposition

• The process of dividing sequential algorithm into
  independent tasklets.
• Expose optimum concurrency.
• PFract Tasklet is computation of a single point
  on a line YYi.
• Rationale Independent of all other points.

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Assignment

• Assign tasklets to compute processes
• Workload balancing
• Minimum communication volume
• PFract Dynamic assignment policy.
• Given one Yi value, slave calculates all X values
  on the line YYi.
• Rationale Minimum Assignment latency

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Orchestration

• Management of parallel execution.
• Communication and Synchronization.
• Topological ordering.
• Spatial Locality.
• The PFract PCOP protocol.
• Point to Point and Global communication and
  synchronization.

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Mapping

• Scheduling of processes on processors.
• Exploit Network Topology.
• Minimum artifactual communication.
• PFract SIMD Process Distinction.
• Multiple Compute Processes.
• One Control Process.

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Result Collection and Display

• Aggregation of computed results.
• Compute processes send computed values.
• Control process receive results.
• Differential calculation rate.
• First-come First-Served basis.
• Displayed as a 2D fractal image.

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PFractMasterSlave Architecture
User Interface
Params
Fractal
Parallelization Engine
Tasklets
Results
Network Communication Manager
R1
Rn
R2
R3
T2
T3
T1
Tn
Node 1
Node 2
Node 3
Node n
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Parallelized Algorithm

• Send Yi to Node Nj and mark node as USED.
• At Nj compute all X values on YYi and return
  results.
• Accept results and mark node as FREE.
• If all nodes are USED wait for results on FCFS
  basis.
• Generate fractal progressively.

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PCOP

• Parallel Cluster Orchestration Protocol
• Reliable and Connection Oriented.
• Command and Reply Messages.
• Synchronous and Asynchronous communication.
• Error Handling and Reporting.
• Cluster Monitoring.

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The PCOP API
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PCOP Implementation
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PFract Features

• Built on BSD sockets library provided by Linux.
• Full color Qt based KDE GUI.
• Object Oriented Design.
• Generic architecture.
• Multi-threaded server.
• Dynamic node reconfiguration.

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A Performance Estimate
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Conclusion

• Advantages of Linux Clusters.
• Scalability.
• Off-the-shelf design.
• Flexibility of the Linux OS.
• Large scale Parallel Computing.
• Generic software architecture.
• Demonstrated using the PFract application.

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Q A
The Mandelbrot Set - Generated by the PFract
Parallel Fractal Generator