Listing All Maximal Cliques in Sparse Graphs in Near-Optimal Time

Eppstein, David; Löffler, Maarten; Strash, Darren

doi:10.1007/978-3-642-17517-6_36

Cited by 277 publications

(283 citation statements)

References 51 publications

(101 reference statements)

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“…A maximal clique is a fully connected subgraph which is not a subset of any other cliques. To find maximal cliques in a network, we use the method proposed by Eppstein et al [49] which is fast and efficient. Because the method is applied only on the ego network of the node with maximum in-community degree and not on the whole network, we can assure that the total running time of leader detection process would be short.…”

Section: Detecting Community Leadersmentioning

confidence: 99%

Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership

Javadi

Gharani

Khadivi

2018

Studies in Systems, Decision and Control

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Abstract-Detecting community structure in social networks is a fundamental problem empowering us to identify groups of actors with similar interests. There have been extensive works focusing on finding communities in static networks, however, in reality, due to dynamic nature of social networks, they are evolving continuously. Ignoring the dynamic aspect of social networks, neither allows us to capture evolutionary behavior of the network nor to predict the future status of individuals. Aside from being dynamic, another significant characteristic of realworld social networks is the presence of leaders, i.e. nodes with high degree centrality having a high attraction to absorb other members and hence to form a local community. In this paper, we devised an efficient method to incrementally detect communities in highly dynamic social networks using the intuitive idea of importance and persistence of community leaders over time. Our proposed method is able to find new communities based on the previous structure of the network without recomputing them from scratch. This unique feature, enables us to efficiently detect and track communities over time rapidly. Experimental results on the synthetic and real-world social networks demonstrate that our method is both effective and efficient in discovering communities in dynamic social networks.

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Section: Detecting Community Leadersmentioning

confidence: 99%

Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership

Javadi

Gharani

Khadivi

2018

Studies in Systems, Decision and Control

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“…An early work due to Bron and Kerbosch [4] is an algorithm based on depth-first-search with good experimental performance on typical inputs, but whose worst case behavior is poor. Other algorithms stemming from this work include [23,40,5,13]. Some of these algorithms, especially [40,13], have asymptotically near-optimal worst case performance, and also run fast on typical inputs.…”

Section: Related Workmentioning

confidence: 99%

“…Other algorithms stemming from this work include [23,40,5,13]. Some of these algorithms, especially [40,13], have asymptotically near-optimal worst case performance, and also run fast on typical inputs. The number of maximal cliques in a graph can be exponential in the number of vertices [34], although this is not true in the typical case.…”

Section: Related Workmentioning

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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“…Second, the otherwise notoriously hard Clique problem is much easier on sparse graphs. For example, all maximal cliques can be enumerated in O(d 3/d · d · n) time on graphs with degeneracy d [9].…”

Section: Introductionmentioning

confidence: 99%

Finding Dense Subgraphs of Sparse Graphs

Komusiewicz

Sorge

2012

Parameterized and Exact Computation

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Abstract. We investigate the computational complexity of the Densestk-Subgraph (DkS) problem, where the input is an undirected graph G = (V, E) and one wants to find a subgraph on exactly k vertices with a maximum number of edges. We extend previous work on DkS by studying its parameterized complexity. On the positive side, we show that, when fixing some constant minimum density µ of the sought subgraph, DkS becomes fixed-parameter tractable with respect to either of the parameters maximum degree and h-index of G. Furthermore, we obtain a fixedparameter algorithm for DkS with respect to the combined parameter "degeneracy of G and |V | − k". On the negative side, we find that DkS is W[1]-hard with respect to the combined parameter "solution size k and degeneracy of G". We furthermore strengthen a previous hardness result for DkS [Cai, Comput. J., 2008] by showing that for every fixed µ, 0 < µ < 1, the problem of deciding whether G contains a subgraph of density at least µ is W[1]-hard with respect to the parameter |V | − k.

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Listing All Maximal Cliques in Sparse Graphs in Near-Optimal Time

Cited by 277 publications

References 51 publications

Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership

Detecting Community Structure in Dynamic Social Networks Using the Concept of Leadership

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

Finding Dense Subgraphs of Sparse Graphs

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