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Clique Counting in MapReduce

Irene Finocchi, Marco Finocchi, Emanuele G. Fusco
2015 ACM Journal of Experimental Algorithmics  
Clique counting is essential in a variety of applications, among which social network analysis.  ...  We tackle the problem of counting the number of k-cliques in large-scale graphs, for any constant k > 3.  ...  In this paper we tackle the problem of counting the number of k-cliques in large-scale graphs, for any small constant k ≥ 3, designing exact and approximate MapReduce algorithms for this problem.  ... 
doi:10.1145/2794080 fatcat:hjibwlgr5za75dbcz3hymkavsy

Spectral Analysis for Billion-Scale Graphs: Discoveries and Implementation [chapter]

U Kang, Brendan Meeder, Christos Faloutsos
2011 Lecture Notes in Computer Science  
Are there nodes that participate in too many or too few triangles? Are there close-knit near-cliques?  ...  We implement HEIGEN and run it on the M45 cluster, one of the top 50 supercomputers in the world.  ...  Additionally, the extreme nodes in the spokes belong to cliques or bi-cliques. Triangle Counting Given a particular node in a graph, how are its neighbors connected? Do they form stars? Cliques?  ... 
doi:10.1007/978-3-642-20847-8_2 fatcat:owpg3prm6ramdfjll74dlhmzxy

Lessons from the Congested Clique Applied to MapReduce [article]

James W. Hegeman, Sriram V. Pemmaraju
2014 arXiv   pre-print
Our simulation algorithm illustrates a natural correspondence between per-node bandwidth in the Congested Clique model and memory per machine in the MapReduce model.  ...  Applying the simulation theorem to the Congested-Clique O(Δ)-coloring algorithm yields an O(1)-round O(Δ)-coloring algorithm in the MapReduce model.  ...  Each of the two tasks mentioned above can be implemented in a (small) constant number of MapReduce rounds as follows.  ... 
arXiv:1405.4356v2 fatcat:vabcraojond3fe5454fv6c3ve4

Lessons from the Congested Clique applied to MapReduce

James W. Hegeman, Sriram V. Pemmaraju
2015 Theoretical Computer Science  
While both of these results are new, what we wish to emphasize in this paper is the simulation of Congested Clique algorithms in the MapReduce model.  ...  in the MapReduce model.  ...  In this way, each reducer in Reduce phase j + 1 can come to know all n message counts for each node u ∈ V . • Reduce phase j + 1: In Reduce phase j + 1, each reducer receives all n message counts (for  ... 
doi:10.1016/j.tcs.2015.09.029 fatcat:ilijmw3ebzf35icintfyarstfu

Lessons from the Congested Clique Applied to MapReduce [chapter]

James W. Hegeman, Sriram V. Pemmaraju
2014 Lecture Notes in Computer Science  
While both of these results are new, what we wish to emphasize in this paper is the simulation of Congested Clique algorithms in the MapReduce model.  ...  in the MapReduce model.  ...  In this way, each reducer in Reduce phase j + 1 can come to know all n message counts for each node u ∈ V . • Reduce phase j + 1: In Reduce phase j + 1, each reducer receives all n message counts (for  ... 
doi:10.1007/978-3-319-09620-9_13 fatcat:wkguq72akzhibpwxungmjdfhqe

A Fast and Provable Method for Estimating Clique Counts Using Turán's Theorem

Shweta Jain, C. Seshadhri
2017 Proceedings of the 26th International Conference on World Wide Web - WWW '17  
Clique counts reveal important properties about the structure of massive graphs, especially social networks.  ...  We define a combinatorial structure called a Turán shadow, the construction of which leads to fast algorithms for clique counting.  ...  Clique counting overall reduces to clique counting in each of these egonets, and this can be parallelized using MapReduce.  ... 
doi:10.1145/3038912.3052636 dblp:conf/www/JainS17 fatcat:xyvnfazntzfmno2hpwdaxtve2q

A Fast and Provable Method for Estimating Clique Counts Using Turán's Theorem [article]

Shweta Jain, C. Seshadhri
2018 arXiv   pre-print
Clique counts reveal important properties about the structure of massive graphs, especially social networks.  ...  We define a combinatorial structure called a Tur\'an shadow, the construction of which leads to fast algorithms for clique counting.  ...  Clique counting overall reduces to clique counting in each of these egonets, and this can be parallelized using MapReduce.  ... 
arXiv:1611.05561v3 fatcat:jzhxmsks3jdnpae7y3dnf2g53u

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

Michael Svendsen, Arko Provo Mukherjee, Srikanta Tirthapura
2015 Journal of Parallel and Distributed Computing  
We present a new parallel algorithm for MCE, Parallel Enumeration of Cliques using Ordering (PECO), designed for the MapReduce framework.  ...  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  ...  Acknowledgments This work was funded in part by the National Science Foundation through grants 0834743 and 0831903, and through a gift from Northrop Grumman Corporation.  ... 
doi:10.1016/j.jpdc.2014.08.011 fatcat:zdjxdmwr6jf7fn3detaxkgfv3e

How to apply de Bruijn graphs to genome assembly

Phillip E C Compeau, Pavel A Pevzner, Glenn Tesler
2011 Nature Biotechnology  
algorithm that minimizes communication is the simple word-count pattern described in the seminal MapReduce article by Google [21] . e algorithm counts the occurrence of every word in a large corpus of  ...  An interesting structure emerges where two of the largest cliques around the predicates connect and counting share the words vertex, thus tying any pair of vertices in this structure by two edges or less  ... 
doi:10.1038/nbt.2023 pmid:22068540 pmcid:PMC5531759 fatcat:yvbmxbd2pnbg5ojtaqggieuiia

The K-clique Densest Subgraph Problem

Charalampos Tsourakakis
2015 Proceedings of the 24th International Conference on World Wide Web - WWW '15  
An interesting consequence of our work is that triangle counting, a well-studied computational problem in the context of social network analysis can be used to detect large near-cliques.  ...  However, frequently the densest subgraph problem fails in detecting large near-cliques in networks. In this work, we introduce the k-clique densest subgraph problem, k ≥ 2.  ...  The algorithm requires O(log(n)/ǫ) rounds and is MapReduce efficient [39] due to the existence of efficient MapReduce triangle counting algorithms, e.g., [48] .  ... 
doi:10.1145/2736277.2741098 dblp:conf/www/Tsourakakis15a fatcat:ci6ccipmljen7hwrviltesnv2y

Mining Association Rules in Various Computing Environments: A Survey [article]

Sudhakar Singh, Pankaj Singh, Rakhi Garg, P. K. Mishra
2019 arXiv   pre-print
There are so many ARM algorithms have been designed that their counting is a large number. In this paper we have surveyed the various ARM algorithms in four computing environments.  ...  In NPA, candidates are replicated across all the processors. Each processor counts support locally and finally global support counting is performed by a coordinator processor.  ...  Eclat, MaxEclat, Clique, MaxClique algorithms are based on equivalence classes & hypergraph clique clustering and lattice traversal schemes.  ... 
arXiv:1908.07918v1 fatcat:uzt4vtybcnh67fdy476qjbdhxy

A Novel Approach to Finding Near-Cliques: The Triangle-Densest Subgraph Problem [article]

Charalampos E. Tsourakakis
2014 arXiv   pre-print
in polynomial time but for many networks fails to find subgraphs which are near-cliques.  ...  In this work, we propose a formulation which combines the best of both worlds: it is solvable in polynomial time and finds near-cliques when the DSP fails.  ...  Acknowledgements I would like to thank Clifford Stein for pointing out that we may use [AOST94] in the place of other max flow algorithms to obtain a faster algorithm.  ... 
arXiv:1405.1477v3 fatcat:pddjp6dj6nezjhnofj2hh3qbaq

HEigen: Spectral Analysis for Billion-Scale Graphs

U Kang, Brendan Meeder, Evangelos E. Papalexakis, Christos Faloutsos
2014 IEEE Transactions on Knowledge and Data Engineering  
Are there nodes that participate in too many or too few triangles? Are there close-knit near-cliques?  ...  We implement HEIGEN and run it on the M45 cluster, one of the top 50 supercomputers in the world.  ...  Additionally, the extreme nodes in the spokes belong to cliques or core-peripheries. Triangle Counting Given a particular node in a graph, how are its neighbors connected? Do they form stars?  ... 
doi:10.1109/tkde.2012.244 fatcat:sxogvibd7rb5roa55uhke5pbfa

Conceptualization with Incremental Bron-Kerbosch Algorithm in Big Data Architecture

2016 Acta Polytechnica Hungarica  
The analysis of the clique detection algorithm in MapReduce architecture provides efficiency comparison for large scale contexts.  ...  The proposed method uses a concept generation module based on clique detection in the context graph.  ...  We tested the two approaches on randomly generated graphs with fixed node counts and edge probabilities to verify their correctness in practice.  ... 
doi:10.12700/aph.13.2.2016.2.8 fatcat:op44d4t6rvaj7o3isf7tb7waiu

Design and evaluation of a novel dataflow based bigdata solution

Yao Wu, Long Zheng, Brian Heilig, Guang R. Gao
2015 Proceedings of the Sixth International Workshop on Programming Models and Applications for Multicores and Manycores - PMAM '15  
One of the most successful system is Hadoop which uses MapReduce as programming/execution model and takes disks as intermedia to process huge volume of data.  ...  With more speicifications, HAMR is fully designed based on In-Memory computing to reduce the unnecessary disk access overhead; task scheduling and memory management are in fine-grain manner to explore  ...  Note that the input graph of K-Cliques is small (2 18 vertices and 7612608 edges) that may limit parallel IO advantage of Hadoop.  ... 
doi:10.1145/2712386.2712397 dblp:conf/ppopp/WuZHG15 fatcat:27vty75xined5h23xzcf7zax3i
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