Dissertation/Thesis Abstract

Multilevel Solution of the Discrete Screened Poisson Equation for Graph Partitioning
by Labra Bahena, Luis R., M.S., California State University, Long Beach, 2017, 104; 10638940
Abstract (Summary)

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.

Indexing (document details)
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
Source Type: DISSERTATION
Subjects: Applied Mathematics, Mathematics
Keywords: Discrete screened poisson equation, Graph partitioning, Multilevel solution
Publication Number: 10638940
ISBN: 978-0-355-52947-0
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