Outline of Material for Test #3

General Algorithm Analysis Knowledge

• Be able to compute timings for algorithms using the network model.
• Be prepared to use standard communication algorithms (broadcast, reduction, etc) when describing and analyzing parallel algorithms
• Be prepared to perform isoefficiency and cost optimality analysis on any of the algorithms covered in the sorting and matrix chapters.
• In short, you are responsible for the basic analysis knowledge that we have covered in Test#2

Parallel Sorting Algorithms

• Fundamentals
• Be able to define internal and external sorting algorithms.
• What is the compare-exchange operation? How is it implemented in parallel
• What is the compare-split operation? How much time does it require?
• What is a comparator? How do you draw one? What is a increasing or decreasing comparator and how do you represent it (draw it).
• Sorting Networks
• Be able to define a bitonic sequence, bitonic split and bitonic merge.
• What is a bitonic merging network? What does it do? What is its size? What is its depth? What does it look like?
• What is a bitonic sorting network? What does it do? What is its size? What is its depth? What does it look like?
• How do we map a bitonic sorting network onto a hypercube? What does the communication patterns look like?
• Be able to derive execution times for the bitonic sorting algorithm on a hypercube architecture. Be able to discuss both mapping one element per processor and many elements per processor.
• Be able to perform a scalability analysis of the bitonic sorting algorithm on the hypercube architecture.
• Quick-sort
• Why is it difficult to develop an efficient parallel quick-sort algorithm by simply running independent subproblems in parallel?
• For the shared memory quicksort algorithm, how is the array partitioned?
• For the shared memory quicksort algorithm, how is load balanced?
• What is the prefix sum operation used for in the shared memory quicksort algorithm?
• Be able to derive the running time of the quicksort algorithm.
• Be able to derive the iso-efficiency function of the quicksort algorithm.
• How do we modify the shared memory quicksort algorithm to generate a message-passing formulation?
• How does pivot selection affect the algorithm performance? Is pivot selection more or less important for parallel quicksort? Why?
• Sample Sort
• What are splitters?
• How large a sample is selected to find the splitters?
• What communication operation is used after the splitters have been found?
• What are the steps in the sample sort algorithm?
• What is the serial and parallel run time of this algorithm
• As described in the text
• Using a bitonic sort to sort the splitters
• What is the isoefficiency function of this sorting algorithm?

Parallel Matrix Algorithms

• What is one dimensional and two dimensional partitioning?
• Be able to describe and analyze one dimensional partitioned dense matrix vector multiplication for both row and column decomposition.
• Review the concurrency constraints on the isoefficiency function. Be able to derive the isoefficiency bounds due to concurrency for all of the parallel matrix algorithms.
• Be able to describe and analyze the two dimensional partitioned dense matrix vector multiplication algorithm.
• Be able to describe and analyze the simple (naive) dense matrix-matrix multiplication algorithm.
• Be able to describe and analyze Cannon's algorithm for dense matrix-matrix multiplication.
• Be able to describe and analyze the DNS algorithm for matrix-matrix multiplication.
• Be able to compare and contrast various algorithms (from the set above) for dense matrix-matrix multiply.