A Parallel Algorithm for Enumerating All Maximal Cliques in Complex Network

Du, Nan; Wu, Bin; Xu, Liutong; Bai, Wei; Pei, Xin

doi:10.1109/icdmw.2006.17

Cited by 53 publications

(38 citation statements)

References 8 publications

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“…Early works in the area of parallel MCE include Zhang et al [45] and Du et al [12]. Zhang et al developed an algorithm based on the Kose et al [24] algorithm.…”

Section: Related Workmentioning

confidence: 99%

“…Since these algorithms are based on breadth first search, they are able to enumerate maximal cliques in increasing order of size, but this makes the memory requirements very large. Du et al [12], present a parallel algorithm based on the output-sensitive class of algorithms. However, as also noted by Schmidt et al [38], this algorithm suffers from poor load balance; the graphs addressed by these experiments are quite small, they have about 150,000 maximal cliques and a million edges.…”

Section: Related Workmentioning

confidence: 99%

“…While our algorithm maybe more broadly applicable, in this work we focus our implementation on the widely used MapReduce [10,11,17] framework for cluster computing. While MCE is widely studied in the sequential setting [4,5,8,25,13,23,21,31,40,41], there is relatively less work on parallel methods [45,12,38,43,30].…”

Section: Introductionmentioning

confidence: 99%

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Mining maximal cliques from a large graph using MapReduce: Tackling highly uneven subproblem sizes

Svendsen

Mukherjee

Tirthapura

2015

Journal of Parallel and Distributed Computing

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We consider Maximal Clique Enumeration (MCE) from a large graph. A maximal clique is perhaps the most fundamental dense substructure in a graph, and MCE is an important tool to discover densely connected subgraphs, with numerous applications to data mining on web graphs, social networks, and biological networks. While effective sequential methods for MCE are known, scalable parallel methods for MCE are still lacking.We present a new parallel algorithm for MCE, Parallel Enumeration of Cliques using Ordering (PECO" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; maxwidth: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">PECO), designed for the MapReduce framework. Unlike previous works, which required a post-processing step to remove duplicate and non-maximal cliques, PECO" role="presentation" style="boxsizing: border-box; display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; wordwrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; minwidth: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">PECOenumerates only maximal cliques with no duplicates. The key technical ingredient is a total ordering of the vertices of the graph which is used in a novel way to achieve a load balanced distribution of work, and to eliminate redundant work among processors. We implemented PECO" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">PECO on Hadoop MapReduce, and our experiments on a cluster show that the algorithm can effectively process a variety of large real-world graphs with millions of vertices and tens of millions of maximal cliques, and scales well with the degree of available parallelism. KeywordsGraph mining, Maximal clique enumeration, Enumeration algorithm, MapReduce, Hadoop, Parallel algorithm, Clique, Load balancing Disciplines Electrical and Computer EngineeringComments This is a manuscript of an article from Svendsen, Michael, Arko Provo Mukherjee, and Srikanta Tirthapura. "Mining maximal cliques from a large graph using mapreduce: Tackling highly uneven subproblem sizes. h i g h l i g h t s• Scalable method for enumerating maximal cliques in a graph using MapReduce.• Effective solution to load balancing.• Experimental evaluation of our solution on large real world graphs.• Outperforms previous MapReduce solutions by orders of magnitude. a r t i c l e i n f o b s t r a c tWe consider Maximal Clique Enumeration (MCE) from a large graph. A maximal clique is perhaps the most fundamental dense substru...

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“…Early works in the area of parallel MCE include Zhang et al [45] and Du et al [12]. Zhang et al developed an algorithm based on the Kose et al [24] algorithm.…”

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Mining maximal cliques from a large graph using MapReduce: Tackling highly uneven subproblem sizes

Svendsen

Mukherjee

Tirthapura

2015

Journal of Parallel and Distributed Computing

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show abstract

“…Due to the increasing popularity of the MapReduce framework, the solutions have been proposed to parallelize maximal clique detection on MapReduce [13,23,38]. They proposed to distribute the vertices across workers and compute every vertex's maximal cliques in parallel.…”

Section: Related Workmentioning

confidence: 99%

“…Updating GðcandÞ with Gðcand À Þ (Lines 11-12), it then iteratively invokes the partition operation to search for the maximal cliques in Gðcand À Þ until Gðcand À Þ becomes a clique (Lines 4-12). After Gðcand À Þ becomes a clique, the algorithm checks whether it is maximal (Lines [13][14].…”

Section: Gp Algorithmmentioning

confidence: 99%

Efficient Maximal Clique Enumeration Over Graph Data

et al. 2016

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In a wide variety of emerging data-intensive applications, such as social network analysis, Web document clustering, entity resolution, and detection of consistently coexpressed genes in systems biology, the detection of dense subgraphs (cliques) is an essential component. Unfortunately, this problem is NP-Complete and thus computationally intensive at scale-hence there is a need for efficient processing, as well as the techniques for distributing the computation across multiple machines such that the computation, which is too time-consuming on a single machine, can be efficiently performed on a machine cluster given that it is large enough. In this paper, we propose a new algorithm (called GP) for maximal clique enumeration. It identifies cliques by the operation of binary graph partitioning, which iteratively divides a graph until each task is sufficiently small to be processed in parallel. Given a connected graph G ¼ ðV; EÞ, the GP algorithm has a space complexity of O(|E|) and a time complexity of OðjEjlðGÞÞ, where lðGÞ represents the number of different cliques existing in G. We also present a hybrid algorithm, which can effectively leverage the advantages of both the GP algorithm and the classical Bron-and-Kerbosch (BK) algorithm. Then, we develop corresponding parallel solutions based on the GP and hybrid algorithms. Finally, we evaluate the performance of the proposed solutions on real and synthetic graph data. Our extensive experiments show that in both centralized and parallel setting, our proposed GP and hybrid approaches achieve considerably better performance than the state-ofthe-art BK approach. Our parallel solutions are implemented and evaluated on MapReduce, a popular shared-nothing parallel framework, but can easily generalize to other sharednothing or shared-memory parallel frameworks.

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Community detection based on social interactions in a social network

Chen

Chuang

Chiu

2014

Asso for Info Science & Tech

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Recent research has involved identifying communities in networks. Traditional methods of community detection usually assume that the network's structural information is fully known, which is not the case in many practical networks. Moreover, most previous community detection algorithms do not differentiate multiple relationships between objects or persons in the real world. In this article, we propose a new approach that utilizes social interaction data (e.g., users' posts on Facebook) to address the community detection problem in Facebook and to find the multiple social groups of a Facebook user. Some advantages to our approach are (a) it does not depend on structural information, (b) it differentiates the various relationships that exist among friends, and (c) it can discover a target user's multiple communities. In the experiment, we detect the community distribution of Facebook users using the proposed method. The experiment shows that our method can achieve the result of having the average scores of Total-Community-Purity and Total-Cluster-Purity both at approximately 0.8.

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A Parallel Algorithm for Enumerating All Maximal Cliques in Complex Network

Cited by 53 publications

References 8 publications

Mining maximal cliques from a large graph using MapReduce: Tackling highly uneven subproblem sizes

Mining maximal cliques from a large graph using MapReduce: Tackling highly uneven subproblem sizes

Efficient Maximal Clique Enumeration Over Graph Data

Community detection based on social interactions in a social network

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