Triangle counting is a fundamental building block in graph algorithms. In this article, we propose a block-based triangle counting algorithm to reduce data movement during both sequential and parallel execution. Our block-based formulation makes the algorithm naturally suitable for heterogeneous architectures. The problem of partitioning the adjacency matrix of a graph is well-studied. Our task decomposition goes one step further: it partitions the set of triangles in the graph. By streaming these small tasks to compute resources, we can solve problems that do not fit on a device. We demonstrate the effectiveness of our approach by providing an implementation on a compute node with multiple sockets, cores and GPUs. The current state-of-the-art in triangle enumeration processes the Friendster graph in 2.1 seconds, not including data copy time between CPU and GPU. Using that metric, our approach is 20 percent faster. When copy times are included, our algorithm takes 3.2 seconds. This is 5.6 times faster than the fastest published CPU-only time.

In today's data-driven world and heterogeneous computing environments, processing large-scale graphs in an architecture agnostic manner has become more crucial than ever before. In terms of graph analytics frameworks, on the one side, there has been a significant interest in developing hand-optimized high-performance computing solutions. On the systems side, following the big data movement and to bring parallel computing to the masses, researchers have proposed several graph processing and management systems to handle large-scale graphs. Hand optimized HPC approaches require high expertise and are expensive to maintain and develop, and graph processing frameworks suffer from limited expressibility and performance. We propose Parallel Graph Algorithms by Blocks (PGAbB), a block-based graph algorithms framework for shared-memory, multi-core, multi-GPU machines. PGAbB offers a sweet spot between efficient parallelism and architecture agnostic algorithm design for a wide class of graph problems while performing close to hand-optimized HPC implementations.

Given two graphs, network alignment asks for a potentially partial mapping between the vertices of the two graphs. This arises in many applications where data from different sources need to be integrated. Recent graph aligners use the global structure of input graphs and additional information given for the edges and vertices. We present SINA, an efficient, shared memory parallel implementation of such an aligner. Our experimental evaluations on a 32-core shared memory machine showed that SINA scales well for aligning large real-world graphs: SINA can achieve up to 28.5× speedup, and can reduce the total execution time of a graph alignment problem with 2M vertices and 100M edges from 4.5 hours to under 10 minutes. To the best of our knowledge, SINA is the first parallel aligner that uses global structure and vertex and edge attributes to handle large graphs.

Integrating data from heterogeneous sources is often modeled as merging graphs. Given two or more "compatible'', but not-isomorphic graphs, the first step is to identify a graph alignment, where a potentially partial mapping of vertices between two graphs is computed. A significant portion of the literature on this problem only takes the global structure of the input graphs into account. Only more recent ones additionally use vertex and edge attributes to achieve a more accurate alignment. However, these methods are not designed to scale to map large graphs arising in many modern applications. We propose a new iterative graph aligner, gsaNA, that uses the global structure of the graphs to significantly reduce the problem size and align large graphs with a minimal loss of information. Concretely, we show that our proposed technique is highly flexible, can be used to achieve higher recall, and it is orders of magnitudes faster than the current state of the art techniques.