Abstract

Link prediction can help rectify inaccuracies in various graph algorithms, stemming from unaccounted-for or overlooked links within networks. However, many existing works use a baseline approach, which incurs unnecessary computational costs due to its high time complexity. Further, many studies focus on smaller graphs, which can lead to misleading conclusions. Here, we study the prediction of links using neighborhood-based similarity measures on large graphs. In particular, we improve upon the baseline approach (IBase), and propose a heuristic approach that additionally disregards large hubs (DLH), based on the idea that high-degree nodes contribute little similarity among their neighbors. On a server equipped with dual 16-core Intel Xeon Gold 6226R processors, DLH is on average 1019x faster than IBase, especially on web graphs and social networks, while maintaining similar prediction accuracy. Notably, DLH achieves a link prediction rate of 38.1M edges/s and improves performance by 1.6x for every doubling of threads.

Abstract

Graphs, including, for example, social networks, collaboration networks, and epidemiological networks, offer a way to represent relationships among entities. Graphs arising from most real-world phenomena are not static and evolve. Dealing with such dynamic graphs requires special algorithms, known as dynamic graph algorithms, that update the required graph analytic based on the change in the current graph instead of recomputing the analytic from scratch. Parallel dynamic graph algorithms are now known for various graph problems such as connectivity, spanning trees, shortest paths, centrality metrics, and community detection. Dynamic algorithms often work in settings where a batch of edge insertions/deletions affects the current graph.

Abstract

Community detection is the problem of identifying natural divisions in networks. Efficient parallel algorithms for identifying such divisions is critical in a number of applications, where the size of datasets have reached significant scales. This paper presents one of the most efficient multicore implementations of the Louvain algorithm, a high quality community detection method. On a server equipped with dual 16-core Intel Xeon Gold 6226R processors, our Louvain, which we term as GVE-Louvain, outperforms Vite, Grappolo, NetworKit Louvain, and cuGraph Louvain (running on NVIDIA A100 GPU) by 50x, 22x, 20x, and 5.8x faster respectively - achieving a processing rate of 560M edges/s on a 3.8B edge graph. In addition, GVE-Louvain improves performance at an average rate of 1.6x for every doubling of threads.

Abstract

PageRank is a widely used centrality measure that assesses the significance of vertices in a graph. Efficiently updating PageRank on dynamic graphs is essential for various applications due to the increasing scale of datasets. This paper introduces our Dynamic Frontier (DF) and Dynamic Frontier with Pruning (DF-P) approaches. Given a batch update comprising edge insertions and deletions, these approaches iteratively identify vertices likely to change their ranks with minimal overhead. On a server featuring a 64-core AMD EPYC-7742 processor, our approaches outperform Static and Dynamic Traversal PageRank by and respectively - on real-world dynamic graphs, and by and on large static graphs with random batch updates. Our approaches scale at a rate of for every doubling of threads.

Abstract

Community detection is the problem of identifying natural divisions in networks. Efficient parallel algorithms for identifying such divisions is critical in a number of applications, where the size of datasets have reached significant scales. This paper presents one of the most efficient implementations of the Leiden algorithm, a high quality community detection method. On a server equipped with dual 16-core Intel Xeon Gold 6226R processors, our Leiden implementation, which we term as GVE-Leiden, outperforms NetworKit Leiden and cuGraph Leiden (running on NVIDIA A100 GPU) by 8.2× and 3.0× respectively — achieving a processing rate of 403M edges/s on a 3.8B edge graph. In addition, GVE-Leiden improves performance at a rate of 1.6× for every doubling of threads.

Abstract

PageRank is a metric that assigns importance to the vertices of a graph based on its neighbors and their scores. Recently, there has been increasing interest in computing PageRank on dynamic graphs, where the graph structure evolves due to edge insertions and deletions. However, traditional barrier-based approaches for updating PageRanks encounter significant wait times on certain graph structures, leading to high overall runtimes. Additionally, the growing trend of multicore architectures with increased core counts has raised concerns about random thread delays and failures. In this study, we propose a lock-free algorithm for updating PageRank scores on dynamic graphs. First, we introduce our Dynamic Frontier (DF) approach, which identifies and processes vertices likely to change PageRanks with minimal overhead. Subsequently, we integrate DF with our lock-free and fault-tolerant PageRank (Alg. DF_LF), incorporating a helping mechanism among threads between its two phases. Experimental results demonstrate that Alg. DF_LF not only eliminates waiting times at iteration barriers but also withstands random thread delays and crashes. On average, it is 4.6x faster than lock-free Naive-dynamic PageRank (Alg. ND_LF).

Abstract

Community detection refers to the identification of coherent partitions in networks. In this poster, we present a parallel dynamic Louvain algorithm that finds communities in rapidly evolving graphs. Given a batch update of edge deletions or insertions, our algorithm identifies an approximate set of affected vertices in the graph with minimal overhead and updates the community membership of each vertex. This process repeats until convergence. Our approach achieves a mean speedup of 7.3x, compared to our parallel and optimized implementation of Delta-screening combined with Louvain, a recently proposed stateof-the-art approach.

Abstract

Community detection is the problem of identifying natural divisions in networks. A relevant challenge in this problem is to find communities on rapidly evolving graphs. In this paper, we present our parallel Dynamic Frontier (DF) approach. Given a batch update of edge deletions or insertions, this approach incrementally identifies an approximate set of affected vertices in the graph with minimal overhead. We apply this approach to both Louvain, a high quality, and Label Propagation Algorithm (LPA), a fast static community detection algorithm. Our approach achieves a mean speedup of 7.3x and 6.7x, when applied to Louvain and LPA respectively, compared to our parallel and optimized implementation of ∆-screening, a recently proposed state-of-the-art approach. Finally, we show how to combine Louvain and LPA with the DF approach to arrive at a hybrid algorithm. This algorithm produces highquality communities while providing a speedup of 2.0x on top of DF-based Louvain.

Abstract

Finding the centrality measures of nodes in a graph is a problem of fundamental importance due to various applications from social networks, biological networks, and transportation networks. Given the large size of such graphs, it is natural to use parallelism as a recourse. Several studies show how to compute the various centrality measures of nodes in a graph on parallel architectures, including multi‐core systems and GPUs. However, as these graphs evolve and change, it is pertinent to study how to update the centrality measures on changes to the underlying graph. In this article, we show novel parallel algorithms for updating the betweenness‐ and closeness‐centrality values of nodes in a dynamic graph. Our algorithms process a batch of updates in parallel by extending the approach of handling a single update for betweenness‐ and closeness‐centrality. For the latter, we also introduce techniques based on

Abstract

Sparse neural networks are shown to give accurate predictions competitive to denser versions, while also minimizing the number of arithmetic operations performed. However current GPU hardware can only exploit structured sparsity patterns for better efficiency. We propose a framework for generating structured multilevel block sparse neural networks by using the theory of graph products. Our Ramanujan bipartite graph product (RBGP) framework uses products of Ramanujan graphs to obtain the best connectivity for a given level of sparsity. This essentially ensures that the i.) the networks has the structured block sparsity for which runtime efficient algorithms exists, ii.) the model gives high prediction accuracy, due to the better expressive power derived from the connectivity of the graph, iii.) the graph data structure has a succinct representation that can be stored efficiently in memory. We use our framework to design a specific connectivity pattern called RBGP4 which makes efficient use of the memory hierarchy available on GPU. We benchmark our approach on image classification and machine translation tasks with an edge (Jetson Nano 2GB) as well as server (V100) GPUs. When compared with commonly used sparsity patterns like unstructured and block, we obtain significant speedups while achieving the same level of accuracy.