Spectral partitioning works: Planar graphs and finite element meshes

Spectral Partitioning Works: Planar Graphs and Finite Element Meshes

Spectral partitioning methods use the Fiedler vector—the eigenvector of the second-smallest eigenvalue of the Laplacian matrix—to find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on bounded-degree pl...

Spectral Partitioning Works: Planar graphs and nite element meshes Preliminary Draft

Spectral partitioning methods use the Fiedler vector|the eigenvector of the secondsmallest eigenvalue of the Laplacian matrix|to nd a small separator of a graph. These methods are important components of many scienti c numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on bounded-degree planar...

Partitioning Well-Clustered Graphs: Spectral Clustering Works!

In this work we study the widely used spectral clustering algorithms, i.e. partition a graph into k clusters via (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and (2) partitioning the embedded points via k-means algorithms. We show that, for a wide class of graphs, spectral clustering algorithms give a good approximatio...

Hybrid Surface Partitioning of Finite Element Meshes

A hybrid automatic and interactive scheme is developed for partitioning the surfaces of mechanical parts represented by finite element meshes on the basis of geometric discontinuity. Given a finite element surface mesh M in three dimensions, the algorithm firstly finds a partition of M into k subregions k M M ,..., 1 on the basis of 1 G discontinuities in an automatic manner. Secondly, an inter...

Eecient Mesh Partitioning for Adaptive Hp Finite Element Meshes