COMP308 Efficient Parallel Algorithms

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COMP308Efficient Parallel Algorithms

• Revision

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COMP 308 Exam

• Time allowed 2.5 hours
• Answer four questions (out of five).
• 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).
• In each question you will see 3 problems which
  usually marked as 10,10 and 5

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Topics

• Sorting Networks
• Communication algorithms
• Parallel Virtual Machine
• Unconventional models and paradigms

• Metrics
• PRAM model
• PRAM algorithms
• Tree algorithms
• Graph algorithms
• Mesh connected networks Sorting

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1. Metrics and basic notions
Sp p

• Parallel time
• Cost
• Efficiency,
• Speed-up,
• Bounds (Amdahl Law)
• --------------------------------------------------
  ----
• Complexity Classes NC, P
• Tractable and intractable problems for parallel
  computers (P-complete problems)

Efficiency
T1 Tp
S( p)
Cost p ? Tp
Upper bound on speedup
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Basics of parallel computing

• 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

• Activation of n processors
• Finding minimum of n numbers
• Sum of elements in an array
• Computing of the first 1 in the sequence of 0s
  and 1s
• 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 (Warshall algorithm)
• Coarse grained vs. Fine grained
• 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
• You need to be able to construct sorting networks

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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

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Unconventional models and paradigms

• Cellular automaton
• Majority problem Rule 184
• Simulation with 2D environment
• Swarm algorithms
• Swarming Characteristics
• Culture model and Adaptive Culture model
• Membrane computing P-systems
• Basic definition,
• Maximal parallelism in membrane computation model
  
• Square function and divisibility
• DNA computing
• Adleman Experiment Hamiltonian Path Problem
• Quantum computations
• Deutsch's problem. Main ideas of quantum
  computations, quantum information.