A Continuous Refinement Strategy for the Multilevel Computation of Vertex Separators
نویسندگان
چکیده
The Vertex Separator Problem (VSP) on a graph is the problem of finding the smallest collection of vertices whose removal separates the graph into two disjoint subsets of roughly equal size. Recently, Hager and Hungerford [1] developed a continuous bilinear programming formulation of the VSP. In this paper, we reinforce the bilinear programming approach with a multilevel scheme for learning the structure of the graph.
منابع مشابه
A Multilevel Vertex Separator Algorithm Based on the Solution of Bilinear Programs
We consider the vertex separator problem on a graph: find a set of vertices of minimum cost whose removal disconnects the graph into two roughly equal sized components. In this talk, we present a multilevel algorithm for the VSP, whose refinement phase is based on the solution of a bilinear program which is shown to approximate the VSP at each level in the multilevel graph hierarchy. We investi...
متن کاملConformal Refinement of Unstructured Quadrilateral Meshes
A multilevel adaptive refinement technique is presented for unstructured quadrilateral meshes in which the mesh is kept conformal at all times. This means that the refined mesh, like the original, is formed of only quadrilateral elements that intersect strictly along edges or at vertices, i.e., vertices of one quadrilateral element do not lie in an edge of another quadrilateral. Elements are re...
متن کاملTowards a Tighter Coupling of Bottom-Up and Top-Down Sparse Matrix Ordering Methods
Most state-of-the-art ordering schemes for sparse matrices are a hybrid of a bottom-up method such as minimum degree and a top down scheme such as George’s nested dissection. In this paper we present an ordering algorithm that achieves a tighter coupling of bottom-up and topdown methods. In our methodology vertex separators are interpreted as the boundaries of the last elements in a bottom-up o...
متن کاملTotal vertex irregularity strength of corona product of some graphs
A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...
متن کاملLimit of Dislocation Density and Ultra-Grain-Refining on Severe Deformation in Iron
It is well-known that severe deformation to metals causes a direct grain refinement of the matrix without special heat-treatments due to the mechanism of dynamic continuous recrystallization (DCR). However, the microstructural revolution during severe deformation is seemed to be different depending on the deformation mode, namely the direction of deformation. In general, multi-directional defor...
متن کامل