Evaluation of Hierarchical Mesh Reorderings

Abstract

Irregular and sparse scientific computing programs frequently experience performance losses due to inefficient use of the memory system in most machines. Previous work has shown that, for a graph model, performing a partitioning and then reordering within each partition improves performance. More recent work has shown that reordering heuristics based on a hypergraph model result in better reorderings than those based on a graph model. This paper studies the effects of hierarchical reordering strategies within the hypergraph model. In our experiments, the reorderings are applied to the nodes and elements of tetrahedral meshes, which are inputs to a mesh optimization application. We show that cache performance degrades over time with consecutive packing, but not with breadth-first ordering, and that hierarchical reorderings involving hypergraph partitioning followed by consecutive packing or breadth-first orderings in each partition improve overall execution time.

A Deviation-Based Dynamic Vertex Reordering Technique for 2D Mesh Quality Improvement

“…Some researchers [12,13] studied the effect of vertex reordering on cache performance. Strout et al [12] developed six reordering methods and applied them to tetrahedral meshes using a hypergraph model. They focused on improving the overall execution time by applying hierarchical data reordering.…”

An approach for code generation in the Sparse Polyhedral Framework

“…Permutation RTRTs that SPF can represent include Cuthill-McKee [14], Reverse Cuthill-McKee [36], breadthfirst [2], Sloan [24], recursive coordinate bisection [70], consecutive packing [19], reordering based on graph partitioning [56,26], hybrid techniques based on graph partitioning and another heuristic within the partition [2,64], reordering based on space-filling curves [39], lexicographical grouping or sorting [15,19,24], and hyper-breadth-first [63]. The reordering algorithms that depend on a mapping of data indices to simulation space coordinate data (e.g., recursive coordinate bisection [70] and space-filling curves [39]) will require additional input be provided to the inspector, but this input can be expressed as an abstract relation.…”

A new metric enabling an exact hypergraph model for the communication volume in distributed-memory parallel applications

“…This additional flexibility of the hypergraph model is exploited in various application areas of parallel computing including sparse matrix-vector multiplication [2], volume rendering [3], and scheduling [4]. Previous work on representing aspects of finite element triangulations using hypergraph models includes partitioning followed by local reorderings within each resulting part of the partitioning in an attempt to improve data locality [5].…”