A second look at counting triangles in graph streams (corrected)

Cormode, Graham; Jowhari, Hossein

doi:10.1016/j.tcs.2016.06.020

Cited by 21 publications

(21 citation statements)

References 11 publications

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“…Defn. 16. Given an edge e = (v, u) in graph G and edge orbit i which lies in pattern H , a match of edge orbit i involving edge (v, u), is a non-induced copy of H in G such that e is mapped to an edge in edge orbit i.…”

Section: Getting Edge Orbit Counts Of 4-vertex Subgraphsmentioning

confidence: 99%

Efficiently Counting Vertex Orbits of All 5-vertex Subgraphs, by EVOKE

Pashanasangi

Seshadhri

2020

Proceedings of the 13th International Conference on Web Search and Data Mining

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Subgraph counting is a fundamental task in network analysis. Typically, algorithmic work is on total counting, where we wish to count the total frequency of a (small) pattern subgraph in a large input data set. But many applications require local counts (also called vertex orbit counts) wherein, for every vertex v of the input graph, one needs the count of the pattern subgraph involving v. This provides a rich set of vertex features that can be used in machine learning tasks, especially classification and clustering. But getting local counts is extremely challenging. Even the easier problem of getting total counts has received much research attention. Local counts require algorithms that get much finer grained information, and the sheer output size makes it difficult to design scalable algorithms.We present EVOKE, a scalable algorithm that can determine vertex orbits counts for all 5-vertex pattern subgraphs. In other words, EVOKE exactly determines, for every vertex v of the input graph and every 5-vertex subgraph H , the number of copies of H that v participates in. EVOKE can process graphs with tens of millions of edges, within an hour on a commodity machine. EVOKE is typically hundreds of times faster than previous state of the art algorithms, and gets results on datasets beyond the reach of previous methods.Theoretically, we generalize a recent "graph cutting" framework to get vertex orbit counts. This framework generate a collection of polynomial equations relating vertex orbit counts of larger subgraphs to those of smaller subgraphs. EVOKE carefully exploits the structure among these equations to rapidly count. We prove and empirically validate that EVOKE only has a small constant factor overhead over the best (total) 5-vertex subgraph counter.

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Section: Getting Edge Orbit Counts Of 4-vertex Subgraphsmentioning

confidence: 99%

Efficiently Counting Vertex Orbits of All 5-vertex Subgraphs, by EVOKE

Pashanasangi

Seshadhri

2020

Proceedings of the 13th International Conference on Web Search and Data Mining

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“…Lower Bounds for Subgraph Counting. There are multiple prior works on memory (space) lower bounds for triangle and subgraph counting in general graphs [9,11,16,53], but not for subgraph counting in bipartite graphs. Since a bipartite graph is more restrictive than a general graph (certain edges are disallowed), lower bounds for unipartite graphs do not directly apply to bipartite graphs.…”

Section: Related Workmentioning

confidence: 99%

Fleet

Sanei-Mehri

Sarıyüce

Tirthapura

2019

Proceedings of the 28th ACM International Conference on Information and Knowledge Management

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We consider space-efficient single-pass estimation of the number of butterflies, a fundamental bipartite graph motif, from a massive bipartite graph stream where each edge represents a connection between entities in two different partitions. We present a space lower bound for any streaming algorithm that can estimate the number of butterflies accurately, as well as FLEET, a suite of algorithms for accurately estimating the number of butterflies in the graph stream. Estimates returned by the algorithms come with provable guarantees on the approximation error, and experiments show good tradeoffs between the space used and the accuracy of approximation. We also present space-efficient algorithms for estimating the number of butterflies within a sliding window of the most recent elements in the stream. While there is a significant body of work on counting subgraphs such as triangles in a unipartite graph stream, our work seems to be one of the few to tackle the case of bipartite graph streams.

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“…Counting the number of triangles in a graph is a fundamental algorithmic problem in the RAM model [4,10,22], streaming [1,2,5,11,13,24,25,26,27,28,33] and the query model [17,21]. In this work, we provide the first approximate triangle counting algorithm using only polylogarithmic queries to a query oracle named Tripartite Independent Set (TIS).…”

Section: Introductionmentioning

confidence: 99%

On Triangle Estimation Using Tripartite Independent Set Queries

et al. 2021

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Estimating the number of triangles in a graph is one of the most fundamental problems in sublinear algorithms. In this work, we provide an approximate triangle counting algorithm using only polylogarithmic queries when the number of triangles on any edge in the graph is polylogarithmically bounded. Our query oracle Tripartite Independent Set (TIS) takes three disjoint sets of vertices A, B and C as input, and answers whether there exists a triangle having one endpoint in each of these three sets. Our query model generally belongs to the class of group queries (Ron and Tsur, ACM ToCT, 2016; Dell and Lapinskas, STOC 2018) and in particular is inspired by the Bipartite Independent Set (BIS) query oracle of Beame et al. (ITCS 2018). We extend the algorithmic framework of Beame et al., with TIS replacing BIS, for triangle counting using ideas from color coding due to Alon et al. (J. ACM, 1995) and a concentration inequality for sums of random variables with bounded dependency (Janson, Rand. Struct. Alg., 2004). ACM Subject ClassificationTheory of computation → Models of computation; Theory of computation → Streaming, sublinear and near linear time algorithms; Mathematics of computing → Probabilistic algorithms

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A second look at counting triangles in graph streams (corrected)

Cited by 21 publications

References 11 publications

Efficiently Counting Vertex Orbits of All 5-vertex Subgraphs, by EVOKE

Efficiently Counting Vertex Orbits of All 5-vertex Subgraphs, by EVOKE

Fleet

On Triangle Estimation Using Tripartite Independent Set Queries

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