Parallel Algorithms

  • Course level: Beginner


Parallel Algorithms. A conventional algorithm uses a single processing element. A parallel algorithm assumes that there are multiple processors.

These processors may communicate with each other using shared memory or an interconnection network. An algorithm designed for a large number (for example, a polynomial in the problem size) of processors can be simulated on a machine with a small number of a processor for a trade-off on time, and therefore is of practical value, while at the same time allowing us to test the limits of parallelism.

Many algorithmic design techniques in the parallel setting will be explored. Parallel complexity theory will also be briefly studied.

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What Will I Learn?

  • Week 1: Theoretical models: PRAM, interconnection networks
  • Week 2: Performance of parallel algorithms, Basic techniques
  • Week 3: Basic techniques
  • Week 4: Comparator Networks.
  • Week 5: Optimal List ranking, applications
  • Week 6: Algorithms for searching, merging, and sorting. Cole’s Merge Sort
  • Week 7: Cole’s Merge Sort(cont’d), Graph algorithms
  • Week 8: Graph algorithms (cont’d)
  • Week 9: Sorting in meshes, Hypercube algorithms, Butterfly network, CCC, Benes network
  • Week 10: Butterfly network, CCC, Benes network etc
  • Week 11: Limits to parallelizability. Lower bounds
  • Week 12: Limits to parallelizability. NC-reductions, P-completeness.

Topics for this course

38 Lessons

Parallel Algorithms

Parallel Algorithms [Intro video]00:00:00
Lec 1: Shared Memory Models – 100:00:00
Lec 2: Shared Memory Models – 200:00:00
Lec 3: Interconnection Networks00:00:00
Lec 4: Cost and Optimality00:00:00
Lec 5: Basic Techniques 100:00:00
Lec 6: Basic Techniques 200:00:00
Lec 7: Basic Techniques 300:00:00
Lec 8: Basic Techniques 41:03:58
Lec 9: Basic Techniques 553:54
Lec 10: Odd Even Merge Sort (OEMS)00:00:00
Lec 11: OEMS, Bitonic-Sort-Merge Sort (BSMS)00:00:00
Lec 12: BSMS, Optimal List Colouring00:00:00
Lec 13: Description00:00:00
Lec 14: Analysis00:00:00
Lec 15: Applications57:08
Lec 16: Applications00:00:00
Lec 17: Fast optimal merge algorithm00:00:00
Lec 18: High level Description00:00:00
Lec19: Cole’s Merge Sort: Details00:00:00
Lec20: Analysis of Cole’s Merge Sort; Lower bound for sorting00:00:00
Lec21: Sorting Lower bound; Connected Components00:00:00
Lec 22: Connected Components (CREW)00:00:00
Lec 23: Connected Components, Vertex Colouring00:00:00
Lec 24: Sorting on a 2D mesh00:00:00
Lec 25: Sorting on a 2D mesh00:00:00
Lec 26: Sorting, Offline routing on a 2D mesh00:00:00
Lec 27: Sorting on a 3D mesh00:00:00
Lec 28: Mesh of Trees, Hypercube00:00:00
Lec 29: Hypercube cont’d00:00:00
Lec 30: Hypercube cont’d, butterfly network00:00:00
Lec 31: Butterfly, CCC and Benes Networks00:00:00
Lec 32: Butterfly, CCC and Benes Networks00:00:00
Lec 33: Shuffle Exchange Graphs, de Bruijn Graphs00:00:00
Lec 34: SEG, dBG (cont’d)00:00:00
Lec 35: Circuit Value Problem is P-complete for NC-reductions00:00:00
Lec 36: Ordered DFS is P-complete for NC-reductions00:00:00
Lec 37: Max Flow is P-complete for NC-reductions00:00:00
Parallel Algorithms

Enrolment validity: Lifetime