Constant-Memory Graph Coarsening

Graph coarsening is an important step for many multi-level algorithms, most notably graph partitioning. However, such methods often utilize an iterative approach, where a new coarser graph representation is explicitly constructed and retained in memory at each level of coarsening. These overheads can be prohibitive for processing massive datasets or in constrained-memory environments like GPUs. We develop a data structure (CM-Graph) for representing coarsened graphs, which can be used with any adjacency-based graph representation. The CM-Graph data structure uses a constant amount of memory, regardless of the desired level of coarsening. In addition, CMGraph does not require modification to the existing graph representation, it offers a several-fold memory savings in practice, and it can even accelerate graph coarsening, due to not having to explicitly construct coarser graph structures. We further describe efficient GPU parallelizations of the CM-Graph subroutines for adjacency access, which can also be utilized in most arbitrary graph computations without modification.