Finding top-k maximal cliques in an uncertain graph

Zou, Zhaonian; Li, Jianzhong; Gao, Hong; Zhang, Shuo

doi:10.1109/icde.2010.5447891

Cited by 86 publications

(55 citation statements)

References 2 publications

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“…Managing and mining uncertain graphs has recently attracted much attention in the database and data mining research community [13,23,24,25]. Especially, Potamias et.…”

Section: Related Workmentioning

confidence: 99%

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Distance-constraint reachability computation in uncertain graphs

et al. 2011

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Driven by the emerging network applications, querying and mining uncertain graphs has become increasingly important. In this paper, we investigate a fundamental problem concerning uncertain graphs, which we call the distance-constraint reachability (DCR) problem: Given two vertices s and t, what is the probability that the distance from s to t is less than or equal to a user-defined threshold d in the uncertain graph? Since this problem is #P-Complete, we focus on efficiently and accurately approximating DCR online. Our main results include two new estimators for the probabilistic reachability. One is a Horvitz-Thomson type estimator based on the unequal probabilistic sampling scheme, and the other is a novel recursive sampling estimator, which effectively combines a deterministic recursive computational procedure with a sampling process to boost the estimation accuracy. Both estimators can produce much smaller variance than the direct sampling estimator, which considers each trial to be either 1 or 0. We also present methods to make these estimators more computationally efficient. The comprehensive experiment evaluation on both real and synthetic datasets demonstrates the efficiency and accuracy of our new estimators.

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“…Managing and mining uncertain graphs has recently attracted much attention in the database and data mining research community [13,23,24,25]. Especially, Potamias et.…”

Section: Related Workmentioning

confidence: 99%

“…Querying and mining uncertain graphs has become an increasingly important research topic [13,24,25]. In the most common uncertain graph model, edges are independent of one another, and each edge is associated with a probability that indicates the likelihood of its existence [13,24].…”

Section: Introductionmentioning

confidence: 99%

Distance-constraint reachability computation in uncertain graphs

et al. 2011

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“…A different approach, and one that has many practical applications, is to return just the smaller, best scoring clusters of the entire graph. One recent paper has focused on finding the top-k maximal cliques in uncertain graphs [32]. However, this method of reducing the search space by finding cliques means many useful real world clusters may be missed, as they may connect strongly but be missing several edges between their nodes.…”

Section: Related Workmentioning

confidence: 99%

Scalable discovery of best clusters on large graphs

Macropol

Singh

2010

Proc. VLDB Endow.

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The identification of clusters, well-connected components in a graph, is useful in many applications from biological function prediction to social community detection. However, finding these clusters can be difficult as graph sizes increase. Most current graph clustering algorithms scale poorly in terms of time or memory. An important insight is that many clustering applications need only the subset of best clusters, and not all clusters in the entire graph. In this paper we propose a new technique, Top Graph Clusters (TopGC), which probabilistically searches large, edge weighted, directed graphs for their best clusters in linear time. The algorithm is inherently parallelizable, and is able to find variable size, overlapping clusters. To increase scalability, a parameter is introduced that controls memory use. When compared with three other state-of-the art clustering techniques, TopGC achieves running time speedups of up to 70% on large scale real world datasets. In addition, the clusters returned by TopGC are consistently found to be better both in calculated score and when compared on real world benchmarks.

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“…Orthogonal to our work, many works extended the definition of clique to other dense subgraph structures (e.g., maximal cliques in an uncertain graph [42], cross-graph quasi-cliques [21], k-truss [20], and densest-subgraph [35]), and studied their applications. The existing algorithms for these problem are centralized.…”

Section: Related Workmentioning

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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Finding top-k maximal cliques in an uncertain graph

Cited by 86 publications

References 2 publications

Distance-constraint reachability computation in uncertain graphs

Distance-constraint reachability computation in uncertain graphs

Scalable discovery of best clusters on large graphs

Efficient Maximal Clique Enumeration Over Graph Data

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