Overview

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Overview

• Efficient Parallel Algorithms
• COMP308

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COMP 308 Exam

• Time allowed 2.5 hours
• Answer four questions (out of six).
• If you attempt to answer more questions than the
  required number of questions, the marks awarded
  for the excess questions will be discarded
  (starting with your lowest mark).

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What will be covered ?

• Basics of parallel computing
• PRAM algorithms
• Basic parallel techniques
• Tree algorithms
• Graph algorithms
• Sorting algorithms
• Parallel Virtual Machine (PVM)
• Communication operations
• Class NC, P and P-complete problems

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1. Basics of parallel computing

• NC complexity class
• Scalability of parallel systems
• Metrics
• Amdahl law
• Optimality and efficiency of parallel algorithms
• Coarse and fine grained computations
• Models
• PRAM model
• EREW, CRCW, CREW, ERCW
• MIMD, SISD, SIMD, MISD
• Network topologies
• Ring, Mesh, Tree, Hypercube

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2. PRAM algorithms

• Finding minimum of n numbers
• Sum of elements in an array
• Computing of the first 1 in the sequence of 0s
  and 1s
• NC sorting algorithm merging sort
• Simulation of CRCW algorithm by EREW model

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3. Basic parallel techniques

• Balanced binary tree technique
• Doubling technique
• Parallel divide and conquer
• The Euler-tour technique

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4. Tree and Graph algorithms

• List ranking problem
• Parallel prefix sum computation
• Parallel algorithms for expression evaluation
• Simultaneous Substitutions Method
• A parallel pebble game
• Parallel Computation of Transitive Closure
  Problem
• Parallel construction of Euler cycles.

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5. Sorting algorithms

• Mesh connected networks.
• Sorting on 1-dim mesh
• Sorting on 2-dim mesh
• Comparison networks
• The zero-one principle
• Bitonic and Merging sorting networks
• Batchers merging network

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6. Parallel Virtual Machine (PVM)

• Basics of Message-Passing Programming
• Broadcast
• Scatter
• Gather
• Reduce

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7. Communication operations

• Store and forward routing
• Cut-through routing
• Broadcasting problem
• Broadcast on ring
• Broadcast on mesh
• Broadcast on tree
• Broadcast on hypercube
• Gossiping problem
• Gossiping on ring
• Gossiping on mesh
• Gossiping on hypercube