Listing All Maximal Cliques in Large Sparse Real-World Graphs

Eppstein, David; Strash, Darren

doi:10.1007/978-3-642-20662-7_31

Cited by 172 publications

(218 citation statements)

References 36 publications

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“…For maximal clique enumeration, the BK algorithm [4] has been widely reported as being faster in practice than its alternatives [15,32]. It is in essence a depth-first search, augmented with pruning tricks.…”

Section: Classical Sequential Algorithmsmentioning

confidence: 99%

“…Due to its NPCompleteness, existing work focused on efficient search. Most of the proposed approaches were based on the classical BK algorithm [4], which has been widely reported as being faster than its alternatives [5,15]. Authors of [10] proposed an efficient algorithm, which was also based on BK search, for maximal clique enumeration with limited memory.…”

Section: Related Workmentioning

confidence: 99%

“…A variant [34] of the BK algorithm also provides a worst-case optimal solution. In practice, the BK algorithm has been widely reported as being faster than its alternatives [5,15].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Classical Sequential Algorithmsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Efficient Maximal Clique Enumeration Over Graph Data

et al. 2016

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“…To solve this MCE problem, several algorithms exist. The most used is Bron Kerbosch [3] for which many enrichment have been proposed such as Tomita [9] or more recently the algorithm of Eppstein et Strash [5]. Because of the NP-hardness of the problem, we do not aim at generating all the possible maximum cliques: our goal is to define a way of obtaining the optimal extension.…”

Section: Extension Generationmentioning

confidence: 99%

Dealing with Incompatibilities During a Knowledge Bases Fusion Process

Amarger

Chanet²,

Haemmerlé

et al. 2016

Graph-Based Representation and Reasoning

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract. More and more data sets are published on the linked open data. Reusing these data is a challenging task as for a given domain, several data sets built for specific usage may exist. In this article we present an approach for existing knowledge bases fusion by taking into account incompatibilities that may appear in their representations. Equivalence mappings established by an alignment tool are considered in order to generate a subset of compatible candidates. The approach has been evaluated by domain experts on datasets dealing with agriculture.

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“…Being linear in the genome length, in practice, is crucial for analyzing the haplotype structure of longer viral or bacterial, or eventually also cancer genomes. It is for this reason, that we have selected this algorithm and prefer it over fast general purpose algorithms for max-clique enumeration in sparse graphs [40,41], which generally scale quadratically with genome length.…”

Section: Max-clique Enumerationmentioning

confidence: 99%

Viral Quasispecies Assembly via Maximal Clique Enumeration

Töpfer

Marschall

Bull

et al. 2014

Lecture Notes in Computer Science

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Virus populations can display high genetic diversity within individual hosts. The intra-host collection of viral haplotypes, called viral quasispecies, is an important determinant of virulence, pathogenesis, and treatment outcome. We present HaploClique, a computational approach to reconstruct the structure of a viral quasispecies from next-generation sequencing data as obtained from bulk sequencing of mixed virus samples. We develop a statistical model for paired-end reads accounting for mutations, insertions, and deletions. Using an iterative maximal clique enumeration approach, read pairs are assembled into haplotypes of increasing length, eventually enabling global haplotype assembly. The performance of our quasispecies assembly method is assessed on simulated data for varying population characteristics and sequencing technology parameters. Owing to its paired-end handling, HaploClique compares favorably to state-of-the-art haplotype inference methods. It can reconstruct error-free full-length haplotypes from low coverage samples and detect large insertions and deletions at low frequencies. We applied HaploClique to sequencing data derived from a clinical hepatitis C virus population of an infected patient and discovered a novel deletion of length 3576167 bp that was validated by two independent long-read sequencing experiments. HaploClique is available at https://github.com/armintoepfer/haploclique. A summary of this

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Listing All Maximal Cliques in Large Sparse Real-World Graphs

Cited by 172 publications

References 36 publications

Efficient Maximal Clique Enumeration Over Graph Data

Efficient Maximal Clique Enumeration Over Graph Data

Dealing with Incompatibilities During a Knowledge Bases Fusion Process

Viral Quasispecies Assembly via Maximal Clique Enumeration

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