A General Graph Model for Representing Exact Communication Volume in Parallel Sparse Matrix-Vector Multiplication

In this paper, we present a new graph model of sparse matrix decomposition for parallel sparse matrix–vector multiplication. Our model differs from previous graph-based approaches in two main respects. Firstly, our model is based on edge colouring rather than vertex partitioning. Secondly, our model is able to correctly quantify and minimise the total communication volume of the parallel sparse matrix– vector multiplication while maintaining the computational load balance across the processors. We show that our graph edge colouring model is equivalent to the fine-grained hypergraph partitioning-based sparse matrix decomposition model. We conjecture that the existence of such a graph model should lead to faster serial and parallel sparse matrix decomposition heuristics and associated tools.