Topics Covered After Midterm

1
Topics Covered After Midterm

• Parallel Sorting
• Parallel Matrix Algorithms
• Parallel Graph Algoritms
• most questions will cover these topics, but will
  use also pre-midterm knowledge
• example question
• give a PRAM algorithm for back substitution

2
Sorting Summary

• Sequential complexity Q(n log n) (comparison
  based)
• Some useful concepts
• Compare Split
• 0-1 Sorting Lemma
• Sorting networks
• Sorting algorithms covered
• Odd-even transposition sort (parallel bubble
  sort)
• Shear sort (sorting algorithm for 2D mesh)
• Bitonic sort (simple, relatively efficient
  sorting network)
• Parallel Quick Sort (no comment)
• Sample Sort (bucket sort variation)

3
Possible Questions

• for which of the following algorithms does 0-1
  Sorting Lemma apply?
• is it true that it applies to all sorting
  networks?
• understand how each of the sorting algorithms
  works
• so you can simulate it on a given input
• you can write pseudocode for it
• understand its strong points and limitations
• perform bitonic split or merge on given
  sequences
• how would you do bitonic sort on a ring network?
  What would be the cost?
• identify the communication patterns used in a
  given sorting algorithm
• given input sequence, what would be the global
  pivots in the sample sort?

4
Matrix Algorithms Summary

• Matrix-Vector Multiplication
• with 1D/2D partitioning
• Matrix-Matrix Multiplication
• simple parallel algorithm
• Cannons algorithm
• the DNS algorithm
• Solving Systems of Linear Equations
• simple Gaussian elimination
• with pipelining/partial pivoting
• back substitution

5
Matrix Algorithms Possible Questions

• understand how each algorithm works
• be able to simulate it
• write pseudocode for processor pi (or pi,j)
• determine communication patterns and costs
• memory requirements/efficiency
• load balancing issues

6
Graph Algorithms

• Minimal Spanning Tree
• Prims algorithm
• Shortest Paths
• single source Dijkstras algorithm
• all- pair Dijkstras, Floyds algorithm
• Transitive Closure
• modified Floyds algorithm
• Connected Components
• merging partial forests
• Algorithms for Sparse Graphs
• maximal independent set Lubys algotihm
• single source shortest paths discussion on
  Johnsons algorithm

7
Graph Algorithms Possible Questions

• Understand the algorithms
• be able to simulate them
• write pseudocode
• be able to apply the techniques to similar
  problems