Lecture 14

Learning objectives

After this class, you should be able to:

1. Explain the purpose of domain decomposition in parallel computing, and justify the graph partitioning model for it.
2. Describe the limitations of the edge-cut metric, and suggest improvements to it.
3. Given a graph, determine its Laplacian.
4. Justify the use of the spectral method for graph partitioning, by showing it as a relaxation of a discrete optimization problem.
5. Given the Fiedler vector for a graph, show how the nodes would be bisected in the first step of the spectral algorithm.

Reading assignment

1. Handout on Domain decomposition: Slides 1-4, 11, 19-22.
2. Read about the purpose of a cache, and how it helps reduce memory access time. You can find this information in any undergraduate computer architecture book, or on the web.

Exercises and review questions

• Questions on current lecture's material
  1. (Post your answer on the discussion board) Suggest some alternatives to the edge-cut metric as a measure of graph partition quality.
  2. Give the Laplacian of a 4x4 mesh.
  3. Show how the spectral method would bisect the graph of slide 15.

• Questions on next lecture's material
  1. Explain what a cache is, and its purpose.