Counting Problems on Graphs: GPU Storage and Parallel Computing Techniques

The availability and utility of large numbers of Graphical Processing Units (GPUs) have enabled parallel computations using extensive multi-threading. Sequential access to global memory and contention at the size-limited shared memory have been main impediments to fully exploiting potential performance in architectures having a massive number of GPUs. We propose novel memory storage and retrieval techniques that enable parallel graph computations to overcome the above issues. More specifically, given a graph G = (V, E) and an integer k <= vertical bar V vertical bar, we provide both storage techniques and algorithms to count the number of: a) connected subgraphs of size k; b) k cliques; and c) k independent sets, all of which can be exponential in number. Our storage technique is based on creating a breadth-first search tree and storing it along with non-tree edges in a novel way. The counting problems mentioned above have many uses, including the analysis of social networks.