Lecture 13

Learning objectives

After this class, you should be able to:

1. Show the steps involved in the iterative parallel prefix algorithm discussed in class, and derive its time complexity.
2. Show how a linear recurrence can be formulated as a parallel prefix problem, and derive the time complexity of the parallel algorithm based on this formulation.
3. Given a matrix, a vector, and the number of processors, show the steps involved in the 1-d and 2-d parallel algorithms, and derive the time complexity of these algorithms.
4. Explain why the 2-d decomposition is more scalable than the 1-d one for matrix-vector multiplication.
5. Explain why we require b and c to have the same data decomposition in the matrix-vector multiplication c = Ab.

Reading assignment

1. Handout on Parallel algorithms: Slides 21 - 30.
2. CLR: pages 529 and 1082.

Exercises and review questions

• Questions on current lecture's material
  1. Give the formal algorithm for iterative parallel prefix and derive its time complexity.
  2. If a linear recurrence had three terms instead of two, then show how we can formulate it as a parallel prefix problem, and derive the time complexity.
  3. (Post your answer on the discussion board) Give an example of a 4x4 matrix and a vector, and show the steps involved in the 2-d parallel algorithm for performing matrix-vector multiplication on four processors.

• Questions on next lecture's material
  1. (Post your answer on the discussion board) Give an example of a connected graph with at least 5 vertices, and show its adjacency matrix.