Related papers: Parallel Triangle Counting in Massive Streaming Gr…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
We present a new algorithm for approximating the number of triangles in a graph $G$ whose edges arrive as an arbitrary order stream. If $m$ is the number of edges in $G$, $T$ the number of triangles, $\Delta_E$ the maximum number of…
Over the last two decades, frameworks for distributed-memory parallel computation, such as MapReduce, Hadoop, Spark and Dryad, have gained significant popularity with the growing prevalence of large network datasets. The Massively Parallel…
The number of triangles (hereafter denoted by $\Delta$) is an important metric to analyze massive graphs. It is also used to compute clustering coefficient in networks. This paper proposes a new algorithm called PES (Priority Edge Sampling)…
In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with $m$ edges and at least $T$ triangles, we show that an extra look over the stream yields a two-pass treaming algorithm…
Triangle counting is a fundamental and widely studied problem on static graphs, and recently on temporal graphs, where edges carry information on the timings of the associated events. Streaming processing and resource efficiency are crucial…
Listing and counting triangles in graphs is a key algorithmic kernel for network analyses including community detection, clustering coefficients, k-trusses, and triangle centrality. We design and implement a new serial algorithm for…
Triangle counting in hypergraph streams, including both hyper-vertex and hyper-edge triangles, is a fundamental problem in hypergraph analytics, with broad applications. However, existing methods face two key limitations: (i) an incomplete…
Triangle counting is an important problem in graph mining. Clustering coefficients of vertices and the transitivity ratio of the graph are two metrics often used in complex network analysis. Furthermore, triangles have been used…
The vast amounts of data used in social, business or traffic networks, biology and other natural sciences are often managed in graph-based data sets, consisting of a few thousand up to billions and trillions of vertices and edges,…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
How can we accurately estimate local triangles for all nodes in simple and multigraph streams? Local triangle counting in a graph stream is one of the most fundamental tasks in graph mining with important applications including anomaly…
This paper investigates parallel random sampling from a potentially-unending data stream whose elements are revealed in a series of element sequences (minibatches). While sampling from a stream was extensively studied sequentially, not much…
We present TRI\`EST, a suite of one-pass streaming algorithms to compute unbiased, low-variance, high-quality approximations of the global and local (i.e., incident to each vertex) number of triangles in a fully-dynamic graph represented as…
Partitioning graphs into blocks of roughly equal size is widely used when processing large graphs. Currently there is a gap in the space of available partitioning algorithms. On the one hand, there are streaming algorithms that have been…
There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even…
One fundamental problem in temporal graph analysis is to count the occurrences of small connected subgraph patterns (i.e., motifs), which benefits a broad range of real-world applications, such as anomaly detection, structure prediction,…
Triangle count and local clustering coefficient are two core metrics for graph analysis. They find broad application in analyses such as community detection and link recommendation. Current state-of-the-art solutions suffer from…
Arrival of multicore systems has enforced a new scenario in computing, the parallel and distributed algorithms are fast replacing the older sequential algorithms, with many challenges of these techniques. The distributed algorithms provide…
Estimating the number of subgraphs in data streams is a fundamental problem that has received great attention in the past decade. In this paper, we give improved streaming algorithms for approximately counting the number of occurrences of…