REPT: A Streaming Algorithm of Approximating Global and Local Triangle Counts in Parallel

Abstract

Recently, considerable efforts have been devoted to approximately computing the global and local (i.e., incident to each node) triangle counts of a large graph stream represented as a sequence of edges. Existing approximate triangle counting algorithms rely on sampling techniques to reduce the computational cost. However, their estimation errors are significantly determined by the covariance between sampled triangles. Moreover, little attention has been paid to developing parallel one-pass streaming algorithms that can be used to fast and approximately count triangles on a multi-core machine or a cluster of machines. To solve these problems, we develop a novel parallel method REPT to significantly reduce the covariance (even completely eliminate the covariance for some cases) between sampled triangles. We theoretically prove that REPT is more accurate than parallelizing existing triangle count estimation algorithms in a direct manner. In addition, we also conduct extensive experiments on a variety of real-world graphs, and the results demonstrate that our method REPT is several times more accurate than state-of-the-art methods. c c i=1τ (i) , where c is the number of processors used for estimating the global triangle count τ . In this case, the arXiv:1811.09136v2 [cs.DS]

TRUST: Triangle Counting Reloaded on GPUs

“…Since triangle counting in extremely large graphs is computationally expensive, some researchers also explore approximate triangle counting algorithms to reduce the runtime [17], [41], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63]. Among them, [54], [58] estimate the number of triangles by sampling the edges, and only counting triangles for the sampled edges.…”

Hypergraph Motifs: Concepts, Algorithms, and Discoveries

“…Due to these wide applications, numerous algorithms have been proposed for rapid and accurate counting of the occurrences of motifs in large graphs. Some of them focus on counting the occurrences of a particular motif, such as the triangle (i.e., clique of three nodes) [2,17,20,21,26,31,33,44,51,52,56,58,59], the butterfly (i.e., 2×2 biclique) [49], and the clique of k nodes [25]. Others are for counting the occurrences of every motif of a fixed size [3,4,7,14,46].…”

Efficient algorithms for subgraph counting and enumeration on large graphs

“…Subgraph counting on streaming graphs is a fundamental problem in graph analysis and has been extensively studied. Due to the online nature and the massive scale of the graph streams, the solutions for this problem always approximate the subgraph counts based on some carefully designed sampling schemes [9,55,62,76,88,99,100,139,140,142,154,165,167,183,190]. All above studies can be categorized into four classes based on two criteria:…”

“…Single pass Fixed space Weight sensitive Fully-dynamic MASCOT [99,100] gSH [8] GPS [9] Triest [142] ThinkD [139,140] WRS [88,138] WSD (Ours) others assume no constraint on the number of sampled edges [55,62,99,100,154,165,183].…”