Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/41035
Title: | Combinatorial Fiedler theory and graph partition |
Author: | Andrade, Enide Dahl, Geir |
Keywords: | Algebraic connectivity Graph partition Sparsest cut L1-norm |
Issue Date: | 15-Apr-2024 |
Publisher: | Elsevier |
Abstract: | Partition problems in graphs are extremely important in applications, as shown in the Data Science and Machine Learning literature. One approach is spectral partitioning based on a Fiedler vector, i.e., an eigenvector corresponding to the second smallest eigenvalue $a(G)$ of the Laplacian matrix $L_G$ of the graph $G$. This problem corresponds to the minimization of a quadratic form associated with $L_G$, under certain constraints involving the $\ell_2$-norm. We introduce and investigate a similar problem, but using the $\ell_1$-norm to measure distances. This leads to a new parameter $b(G)$ as the optimal value. We show that a well-known cut problem arises in this approach, namely the sparsest cut problem. We prove connectivity results and different bounds on this new parameter, relate to Fiedler theory and show explicit expressions for $b(G)$ for trees. We also comment on an $\ell_{\infty}$-norm version of the problem. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/41035 |
DOI: | 10.1016/j.laa.2024.02.005 |
ISSN: | 0024-3795 |
Publisher Version: | https://doi.org/10.1016/j.laa.2024.02.005 |
Appears in Collections: | CIDMA - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
EAGDfile.pdf | 534.51 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.