A Locality Preserving Graph Ordering Approach for Implicit Partitioning: Graph-Filing Curves

Linear orderings defined through space-filling curves are often applied to quickly partition graphs arising in finite element simulations. In applications with constant meshes but a rapidly changing load per element, an ordering has to be determined only once and all subsequent partitionings can be computed very quickly through a simple interval splitting. However, partitionings based on space-filling curves have known drawbacks. Especially when applied to deeply refined meshes or discretizations that contain holes, a high edge-cut is produced. In this paper we present a new linear ordering approach called graph-filling curves. In contrast to space-filling curves, we determine a node ordering based on the graph’s structure rather than on its geometric information. Our experimental evaluation shows that such orderings involving the graphs connectivity information lead to clearly superior implicit partitionings.