A new graph partitioning algorithm which makes use of a novel objective function and seeding strategy, Product Cut, frequently outperforms standard clustering methods. The solution strategy on solving this objective depends on developing a fast solution method for the systems of graph--based analogues of the screened Poisson equation, which is a well-studied problem in the special case of structured graphs arising from PDE discretization.
In this work, we attempt to improve the powerful Algebraic Multigrid (AMG) method and build upon the recently introduced Product Cut algorithm. Specifically, we study the consequences of incorporating a dynamic determination of the diffusion parameter by introducing a prior to the objective function. This culminates in an algorithm which seems to partially eliminate an advantage present in the original Product Cut algorithm's slower implementation.
|Advisor:||Brecht, James H. von|
|Commitee:||Kim, Eun Heui, Lee, Chung-Min|
|School:||California State University, Long Beach|
|Department:||Mathematics and Statistics|
|School Location:||United States -- California|
|Source:||MAI 57/01M(E), Masters Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Discrete screened poisson equation, Graph partitioning, Multilevel solution|
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