Parallel Algorithm for Enumerating Maximal Cliques in Complex Network

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

doi:10.1007/978-3-540-88067-7_12

Cited by 19 publications

(27 citation statements)

References 9 publications

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“…They mainly focus on devising an approximate algorithm (since MCE is an NP-hard problem) for extracting all maximal cliques. The existence of an algorithm for addressing MCE is categorized as: (1) sequential in-memory algorithms [3,4]; (2) sequential I/O efficient algorithms [5,6] which concentrate on reducing the high cost of random disk I/Os for processing graphs that cannot fit in main memory [2]; (3) aiming to reduce the running time-the third type approach is parallel, and distributed algorithms [7,8] are proposed. However, these existing studies usually ignore the formation principle of maximal cliques.…”

Section: Related Workmentioning

confidence: 99%

Exploiting the Formation of Maximal Cliques in Social Networks

2017

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Abstract:In social networking analysis, there exists a fundamental problem called maximal cliques enumeration(MCE), which has been extensively investigated in many fields, including social networks, biological science, etc. As a matter of fact, the formation principle of maximal cliques that can help us to speed up the detection of maximal cliques from social networks is often ignored by most existing research works. Aiming to exploit the formation of maximal cliques in social networks, this paper pioneers a creative research issue on the detection of bases of maximal cliques in social networks. We propose a formal concept analysis-based approach for detecting the bases of maximal cliques and detection theorem. It is believed that our work can provide a new research solution and direction for future topological structure analysis in various complex networking systems.

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Section: Related Workmentioning

confidence: 99%

Exploiting the Formation of Maximal Cliques in Social Networks

2017

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“…Karande 2008; Modani and Dey 2008;Du et al 2009;Schmidt et al 2009] for computing max-cliques essentially construct a search tree in a similar way as does Algorithm 1, although different algorithms have their own ways of pruning unnecessary searches and performing the maximality checking (lines 2 and 4 of Procedure 2).…”

Section: The Set Of H-vertices Of G; ∀V ∈ H D(v)mentioning

confidence: 99%

“…That is, we distribute a B * -graph (instead of the entire graph as do in the existing parallel algorithms [Du et al 2009;Schmidt et al 2009]) to each computing element for maximal clique enumeration, and yet guaranteeing the completeness of result.…”

Section: Base Vertex Selection By Available Memorymentioning

confidence: 99%

“…The optimal worst-case time of backtracking-based maximal clique computation was shown to be O(3 n/3 ) [Tomita et al 2006]. Recently, parallel algorithms [Du et al 2009;Schmidt et al 2009] were proposed to compute maximal cliques from different points of the search tree in parallel. However, all these studies did not focus on reducing the memory complexity and require O(m+ n) memory space in the best case.…”

Section: Related Workmentioning

confidence: 99%

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Finding maximal cliques in massive networks

Cheng

et al. 2011

ACM Trans. Database Syst.

126

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Maximal clique enumeration is a fundamental problem in graph theory and has important applications in many areas such as social network analysis and bioinformatics. The problem is extensively studied; however, the best existing algorithms require memory space linear in the size of the input graph. This has become a serious concern in view of the massive volume of today's fast-growing networks. We propose a general framework for designing external-memory algorithms for maximal clique enumeration in large graphs. The general framework enables maximal clique enumeration to be processed recursively in small subgraphs of the input graph, thus allowing in-memory computation of maximal cliques without the costly random disk access. We prove that the set of cliques obtained by the recursive local computation is both correct (i.e., globally maximal) and complete. The subgraph to be processed each time is defined based on a set of base vertices that can be flexibly chosen to achieve different purposes. We discuss the selection of the base vertices to fully utilize the available memory in order to minimize I/O cost in static graphs, and for update maintenance in dynamic graphs. We also apply our framework to design an external-memory algorithm for maximum clique computation in a large graph.

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“…However, addressing the I/O problem does not solve the main computational issue as MCE is a CPU-intensive task. The third type is parallel and distributed algorithms [24], [26], [27], [28], [29], which aim at reducing the elapsed running time by parallelizing the task of MCE. However, the parallel algorithms [26], [28] require a copy of the entire input graph to be resident in main memory and cannot handle unbalanced workload.…”

Section: Introductionmentioning

confidence: 99%

Distributed Maximal Clique Computation and Management

Cheng

2016

IEEE Trans. Serv. Comput.

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Abstract-Maximal cliques are elementary substructures in a graph and instrumental in graph analysis such as the structural analysis of many complex networks, graph clustering and community detection, network hierarchy detection, emerging pattern mining, vertex importance measures, etc. However, the number of maximal cliques is also notoriously large even for many small real world graphs. This size problem gives rise to challenges in both computing and managing the set of maximal cliques. Many algorithms for computing maximal cliques have been proposed in the literature; however, most of them are sequential algorithms that cannot scale due to the high complexity of the problem, while existing parallel algorithms for computing maximal cliques are mostly immature and especially suffer from skewed workload. As for managing the set of maximal cliques, which is essential due to its large size, there is barely any efficient method for querying or updating the set of maximal cliques. In this paper, we first propose a distributed algorithm built on a share-nothing architecture for computing the set of maximal cliques. We effectively address the problem of skewed workload distribution due to high-degree vertices, which also leads to drastically reduced worst-case time complexity for computing maximal cliques in common real-world graphs. Then, we propose a set of fundamental query operations and efficient algorithms to process the queries, to aid more efficient and effective analysis of the set of maximal cliques. Finally, we also devise algorithms to support efficient update maintenance of the set of maximal cliques when the underlying graph is updated. We verify the efficiency of our algorithms for computing, querying, and updating the set of maximal cliques with a range of real-world graphs from different application domains.

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Parallel Algorithm for Enumerating Maximal Cliques in Complex Network

Cited by 19 publications

References 9 publications

Exploiting the Formation of Maximal Cliques in Social Networks

Exploiting the Formation of Maximal Cliques in Social Networks

Finding maximal cliques in massive networks

Distributed Maximal Clique Computation and Management

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