Tiered sampling: An efficient method for approximate counting sparse motifs in massive graph streams

Stefani, Lorenzo De; Terolli, Erisa; Upfal, Eli

doi:10.1109/bigdata.2017.8257993

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…This is an arbitrary example, similar results can be observed on almost all the motifs and datasets 7. Similar observations hold for PRESTO-E.…”

supporting

confidence: 84%

“…A fundamental problem in the analysis of network motifs is the counting problem [5,2], which requires to output the number of instances of the given topology defining the motif. This challenging computational problem has been extensively studied, with several techniques designed to count the number of occurrences of simple motifs, such as triangles [26,21,24] or sparse motifs [7].…”

Section: Introductionmentioning

confidence: 99%

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PRESTO: Simple and Scalable Sampling Techniques for the Rigorous Approximation of Temporal Motif Counts

Sarpe¹,

Vandin²

2021

Preprint

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The identification and counting of small graph patterns, called network motifs, is a fundamental primitive in the analysis of networks, with application in various domains, from social networks to neuroscience. Several techniques have been designed to count the occurrences of motifs in static networks, with recent work focusing on the computational challenges provided by large networks. Modern networked datasets contain rich information, such as the time at which the events modeled by the networks edges happened, which can provide useful insights into the process modeled by the network. The analysis of motifs in temporal networks, called temporal motifs, is becoming an important component in the analysis of modern networked datasets. Several methods have been recently designed to count the number of instances of temporal motifs in temporal networks, which is even more challenging than its counterpart for static networks. Such methods are either exact, and not applicable to large networks, or approximate, but provide only weak guarantees on the estimates they produce and do not scale to very large networks. In this work we present an efficient and scalable algorithm to obtain rigorous approximations of the count of temporal motifs. Our algorithm is based on a simple but effective sampling approach, which renders our algorithm practical for very large datasets. Our extensive experimental evaluation shows that our algorithm provides estimates of temporal motif counts which are more accurate than the state-of-the-art sampling algorithms, with significantly lower running time than exact approaches, enabling the study of temporal motifs, of size larger than the ones considered in previous works, on billion edges networks.

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“…This is an arbitrary example, similar results can be observed on almost all the motifs and datasets 7. Similar observations hold for PRESTO-E.…”

supporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

PRESTO: Simple and Scalable Sampling Techniques for the Rigorous Approximation of Temporal Motif Counts

Sarpe¹,

Vandin²

2021

Preprint

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“…The above methods considered the triangle counting problem in many different settings, including offline graphs [5,8,20,[48][49][50], insertion-only [1,2,7,18,26,35,41,45,46,48,60] and fully-dynamic [4,42,44] graph streams, sliding windows [11], and distributed graphs [32,34,43]. Moreover, sampling methods were also proposed for estimating more complex motifs than triangles, e.g., 4-vertex motifs [19,39], 5-vertex motifs [36,58,59,61], motifs with 6 or more vertices [3], 𝑘-cliques [6,17], sparse motifs with low counts [47], and butterflies in bipartite graphs [39]. However, all the above methods were not designed for temporal graphs.…”

Section: Subgraph (Motif) Counting In Static Graphsmentioning

confidence: 99%

Efficient Sampling Algorithms for Approximate Temporal Motif Counting

Wang

Jiang

et al. 2020

Proceedings of the 29th ACM International Conference on Information &Amp; Knowledge Management

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A great variety of complex systems ranging from user interactions in communication networks to transactions in financial markets can be modeled as temporal graphs, which consist of a set of vertices and a series of timestamped and directed edges. Temporal motifs in temporal graphs are generalized from subgraph patterns in static graphs which take into account edge orderings and durations in addition to structures. Counting the number of occurrences of temporal motifs is a fundamental problem for temporal network analysis. However, existing methods either cannot support temporal motifs or suffer from performance issues. In this paper, we focus on approximate temporal motif counting via random sampling. We first propose a generic edge sampling (ES) algorithm for estimating the number of instances of any temporal motif. Furthermore, we devise an improved EWS algorithm that hybridizes edge sampling with wedge sampling for counting temporal motifs with 3 vertices and 3 edges. We provide comprehensive analyses of the theoretical bounds and complexities of our proposed algorithms. Finally, we conduct extensive experiments on several real-world datasets, and the results show that our ES and EWS algorithms have higher efficiency, better accuracy, and greater scalability than the state-ofthe-art sampling method for temporal motif counting.

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“…So-called wedge-based methods sample length-2 paths [48], and this concept has been generalized for counting 4-cliques [25]. Finally, tiered-sampling combines sampling of arbitrary subgraphs to count the occurrence of larger graphs (with a focus on 4-cliques and 5-cliques) [53].…”

Section: Additional Related Workmentioning

confidence: 99%

Retrieving Top Weighted Triangles in Graphs

Kumar

Liu

Charikar

et al. 2020

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

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Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of connection between nodes, which are often modeled by a weighted graph, but existing scalable graph algorithms for pattern mining are designed for unweighted graphs. Here, we develop a suite of deterministic and random sampling algorithms that enable the fast discovery of the 3cliques (triangles) with the largest weight in a graph, where weight is measured by a generalized mean of a triangle's edges. For example, one of our proposed algorithms can find the top-1000 weighted triangles of a weighted graph with billions of edges in thirty seconds on a commodity server, which is orders of magnitude faster than existing "fast" enumeration schemes. Our methods thus open the door towards scalable pattern mining in weighted graphs.

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Tiered sampling: An efficient method for approximate counting sparse motifs in massive graph streams

Cited by 5 publications

References 17 publications

PRESTO: Simple and Scalable Sampling Techniques for the Rigorous Approximation of Temporal Motif Counts

PRESTO: Simple and Scalable Sampling Techniques for the Rigorous Approximation of Temporal Motif Counts

Efficient Sampling Algorithms for Approximate Temporal Motif Counting

Retrieving Top Weighted Triangles in Graphs

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