Sampling Triples from Restricted Networks using MCMC Strategy

Rahman, Mahmudur; Hasan, Mohammad Al

doi:10.1145/2661829.2662075

Cited by 14 publications

(19 citation statements)

References 24 publications

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“…However, Rahman et al did not use IS in their solution, they rather have used MH algorithm. Their solution, named Vertex‐MCMC, works as follows: Use MH algorithm to design a random walk whose stationarity distribution

π \sim ((), \begin{matrix} d (() \cdot) \\ 2 \end{matrix})

.…”

Section: Triangle Counting In Restricted Access Scenariomentioning

confidence: 99%

“…We further consider two of the restricted access‐based methods: random walk over nodes with importance weight adjustment hereby named as randWalk _ importance (Eq. (14)), and ‘vertexMCMC’, i.e., MCMC walk over nodes. We implement all the above methods ourself by using identical graph data structures and edge existence query module.…”

Section: Experimental Comparisonsmentioning

confidence: 99%

“…Some variants of triangle counting algorithms have also been inspired by data access constraints. For example, triangle counting algorithms have been proposed for various data access scenarios which are different from traditional random memory access, examples include restricted access, and streaming data access …”

Section: Introductionmentioning

confidence: 99%

“…To achieve efficiency, approximate triangle counting through sampling has been a very active direction in many recent works. [11][12][13][14][15][16] Also, researchers have tried to achieve efficiency through algorithms that run on multi-core or distributed environment. 13,14,17 Some variants of triangle counting algorithms have also been inspired by data access constraints.…”

Section: Introductionmentioning

confidence: 99%

“…13,14,17 Some variants of triangle counting algorithms have also been inspired by data access constraints. For example, triangle counting algorithms have been proposed for various data access scenarios which are different from traditional random memory access, examples include restricted access, 12 and streaming data access. 16,18 Computational complexity of a triangle counting algorithm is a good indicator of its efficiency, but in real-life the execution time of two algorithms can be widely different even if they have the same computational complexity.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Triangle counting in large networks: a review

Hasan

Dave

2017

WIREs Data Min & Knowl

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Counting and enumeration of local topological structures, such as triangles, is an important task for analyzing large real‐life networks. For instance, triangle count in a network is used to compute transitivity—an important property for understanding graph evolution over time. Triangles are also used for various other tasks completed for real‐life networks, including community discovery, link prediction, and spam filtering. The task of triangle counting, though simple, has gained wide attention in recent years from the data mining community. This is due to the fact that most of the existing algorithms for counting triangles do not scale well to very large networks with millions (or even billions) of vertices. To circumvent this limitation, researchers proposed triangle counting methods that approximate the count or run on distributed clusters. In this paper, we discuss the existing methods of triangle counting, ranging from sequential to parallel, single‐machine to distributed, exact to approximate, and off‐line to streaming. We also present experimental results of performance comparison among a set of approximate triangle counting methods built under a unified implementation framework. Finally, we conclude with a discussion of future works in this direction. WIREs Data Mining Knowl Discov 2018, 8:e1226. doi: 10.1002/widm.1226 This article is categorized under: Algorithmic Development > Structure Discovery

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π \sim ((), \begin{matrix} d (() \cdot) \\ 2 \end{matrix})

.…”

Section: Triangle Counting In Restricted Access Scenariomentioning

confidence: 99%

Section: Experimental Comparisonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Triangle counting in large networks: a review

Hasan

Dave

2017

WIREs Data Min & Knowl

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The Role of Graphlets in Viral Processes on Networks

et al. 2018

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Predicting the evolution of viral processes on networks is an important problem with applications arising in biology, the social sciences, and the study of the Internet. In existing works, mean-field analysis based upon degree distribution is used for the prediction of viral spreading across networks of different types. However, it has been shown that degree distribution alone fails to predict the behavior of viruses on some real-world networks and recent attempts have been made to use assortativity to address this shortcoming. In this paper we show that assortativity also fails to adequately predict the spread of viruses for a number of real-world networks. We propose using the graphlet frequency distribution in combination with assortativity to explain variations in the evolution of viral processes across networks with identical degree distribution. Using a data driven approach, by coupling predictive modeling with viral process simulation on real-world networks, we show that simple regression models based on graphlet frequency distribution can explain over 95% of the variance in virality on networks with the same degree distribution but different network topologies. Our results not only highlight the importance of graphlets but also identify a small collection of graphlets which may have the highest influence over the viral processes on a network.

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Butterfly counting and bitruss decomposition on uncertain bipartite graphs

Zhou

Wang²,

Chen

2023

The VLDB Journal

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Uncertain butterflies are one of, if not the, most important graphlet structures on uncertain bipartite networks. In this paper, we examine the uncertain butterfly structure (in which the existential probability of the graphlet is greater than or equal to a threshold parameter), as well as the global Uncertain Butterfly Counting Problem (to count the total number of these instances over an entire network). To solve this task, we propose a non-trivial exact baseline (UBFC), as well as an improved algorithm (IUBFC) which we show to be faster both theoretically and practically. We also design two sampling frameworks (UBS and PES) which can sample either a vertex, edge or wedge from the network uniformly and estimate the global count quickly. Furthermore, a notable butterfly-based community structure which has been examined in the past is the k-bitruss. We adapt this community structure onto the uncertain bipartite graph setting and introduce the Uncertain Bitruss Decomposition Problem (which can be used to directly answer any k-bitruss search query for any k). We then propose an exact algorithm (UBitD) to solve our problem with three variations in deriving the initial uncertain support. Using a range of networks with different edge existential probability distributions, we validate the efficiency and effectiveness of our solutions.

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Sampling Triples from Restricted Networks using MCMC Strategy

Cited by 14 publications

References 24 publications

Triangle counting in large networks: a review

Triangle counting in large networks: a review

The Role of Graphlets in Viral Processes on Networks

Butterfly counting and bitruss decomposition on uncertain bipartite graphs

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