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Distributed Estimation of Graph 4-Profiles

Ethan R. Elenberg, Karthikeyan Shanmugam, Michael Borokhovich, Alexandros G. Dimakis
2016 Proceedings of the 25th International Conference on World Wide Web - WWW '16  
We also study the more complicated problem of estimating the local 4-profiles centered at each vertex of the graph.  ...  We present a novel distributed algorithm for counting all four-node induced subgraphs in a big graph.  ...  At each vertex v, each combinatorial equation relates a linear combination of the local 4-subgraph counts to the count of a pair of 3-subgraphs sharing an edge va.  ... 
doi:10.1145/2872427.2883082 dblp:conf/www/ElenbergSBD16 fatcat:jjthhjhbajebxghx4fqi3lwauq

Estimation of Graphlet Counts in Massive Networks

Ryan A. Rossi, Rong Zhou, Nesreen K. Ahmed
2018 IEEE Transactions on Neural Networks and Learning Systems  
than 1% relative error; (d) scalable and space efficient for massive networks with billions of edges; and (e) effective for a variety of real-world settings as well as estimating global and local graphlet  ...  Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks.  ...  For instance, instead of using PGD [13] to count graphlets (as done in this paper), one can always use the fastest state-of-the-art subgraph counting algorithm.  ... 
doi:10.1109/tnnls.2018.2826529 pmid:29994543 fatcat:ckfw6llcijdmrivjz7h2omaici

Beyond Triangles: A Distributed Framework for Estimating 3-profiles of Large Graphs [article]

Ethan R. Elenberg, Karthikeyan Shanmugam, Michael Borokhovich, Alexandros G. Dimakis
2015 arXiv   pre-print
Further, we study the problem of estimating local and ego 3-profiles, two graph quantities that characterize the local neighborhood of each vertex of a graph.  ...  We study the problem of approximating the 3-profile of a large graph. 3-profiles are generalizations of triangle counts that specify the number of times a small graph appears as an induced subgraph of  ...  [1] develops subgraph estimators for clustering coefficient, triangle count, and wedge count in a streaming sub-sampled graph.  ... 
arXiv:1506.06671v1 fatcat:hr4pbfp6ezffjiwz7sfkz6xmzq

Beyond Triangles

Ethan R. Elenberg, Karthikeyan Shanmugam, Michael Borokhovich, Alexandros G. Dimakis
2015 Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '15  
Further, we study the problem of estimating local and ego 3-profiles, two graph quantities that characterize the local neighborhood of each vertex of a graph.  ...  We study the problem of approximating the 3-profile of a large graph. 3-profiles are generalizations of triangle counts that specify the number of times a small graph appears as an induced subgraph of  ...  [1] develops subgraph estimators for clustering coefficient, triangle count, and wedge count in a streaming sub-sampled graph.  ... 
doi:10.1145/2783258.2783413 dblp:conf/kdd/ElenbergSBD15 fatcat:ccyhwydbebe5jbifh3juuo5fjq

Systematic identification of statistically significant network measures

Etay Ziv, Robin Koytcheff, Manuel Middendorf, Chris Wiggins
2005 Physical Review E  
Key improvements over existing approaches include discovery of "motif-hubs" (multiple overlapping significant subgraphs), computational efficiency relative to subgraph census, and flexibility (the method  ...  ., a set of measures on graphs) for performing statistical analyses of networks.  ...  We thank the organizers of the LANL/CNLS conference on "Networks: Structure, Dynamics, and Function." C.W. was supported in part by NSF Grant No. ECS-0332479, NSF Grant No.  ... 
doi:10.1103/physreve.71.016110 pmid:15697661 fatcat:mscmmn7gsbfqddr6b5lsncljn4

Distributed Estimation of Graph 4-Profiles [article]

Ethan R. Elenberg, Karthikeyan Shanmugam, Michael Borokhovich, Alexandros G. Dimakis
2016 arXiv   pre-print
We also study the more complicated problem of estimating the local 4-profiles centered at each vertex of the graph.  ...  We present a novel distributed algorithm for counting all four-node induced subgraphs in a big graph.  ...  At each vertex v, each combinatorial equation relates a linear combination of the local 4-subgraph counts to the count of a pair of 3-subgraphs sharing an edge va.  ... 
arXiv:1510.02215v2 fatcat:o7nklg5wxjerlhanopepn4vr3u

Technology mapping algorithms for hybrid fpgas containing lookup tables and plas

S. Krishnamoorthy, R. Tessier
2003 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
A breadth-first search-based subgraph extraction and evaluation heuristic is integrated with product term (Pterm) count, area, and delay estimators to guide the technology mapping process.  ...  Present commercial tools, which target these hybrid devices, require hand partitioning of user designs to isolate logic for each type of logic resource.  ...  Since Pterm count must be evaluated for each subgraph, the Pterm count estimator runtime impacts the usability of the estimator.  ... 
doi:10.1109/tcad.2003.810743 fatcat:vp4jmm4pzresfj7gtmvysfshj4

Area-Optimized Technology Mapping for Hybrid FPGAs [chapter]

Srini Krishnamoorthy, Sriram Swaminathan, Russell Tessier
2000 Lecture Notes in Computer Science  
It is shown that fast estimation of post-minimization product term counts plays an especially important role in the mapping of designs to PLAs.  ...  The subgraphs are subsequently mapped to assigned target resources.  ...  product term estimation was outlined that can estimate the post-minimization product term count of a subgraph prior to the application of Espresso.  ... 
doi:10.1007/3-540-44614-1_21 fatcat:pyn3dupgqrbdhfzrmir2756ey4

Clique Counting in MapReduce

Irene Finocchi, Marco Finocchi, Emanuele G. Fusco
2015 ACM Journal of Experimental Algorithmics  
We tackle the problem of counting the number of k-cliques in large-scale graphs, for any constant k > 3.  ...  Clique counting is essential in a variety of applications, among which social network analysis.  ...  The local space and the local running time of mappers and reducers are O(m) and O(m (k−1)/2 ), respectively. • We propose sampling-based estimators that can reduce dramatically the running time and local  ... 
doi:10.1145/2794080 fatcat:hjibwlgr5za75dbcz3hymkavsy

Page 2859 of Mathematical Reviews Vol. , Issue 90E [page]

1990 Mathematical Reviews  
This paper provides central limit theorems for some subgraph counts such as the count of all subgraphs in G,,, of order v and of size s, the count of subgraphs isomorphic to H, the count of induced subgraphs  ...  isomorphic to H, the count of subgraphs with r edges, and so on.  ... 

Counting Arbitrary Subgraphs in Data Streams [chapter]

Daniel M. Kane, Kurt Mehlhorn, Thomas Sauerwald, He Sun
2012 Lecture Notes in Computer Science  
We provide the first non-trivial estimator for approximately counting the number of occurrences of an arbitrary subgraph H of constant size in a (large) graph G.  ...  Prior to this work, only for a few non-regular graphs estimators were known in case of edge-insertions, leaving the problem of counting general subgraphs in the turnstile model wide open.  ...  An Unbiased Estimator for Counting Subgraphs We present a framework for counting general subgraphs.  ... 
doi:10.1007/978-3-642-31585-5_53 fatcat:dcit3yxswjf2fh6ozojicficxe

Estimating Graphlet Statistics via Lifting [article]

Kirill Paramonov, James Sharpnack
2018 arXiv   pre-print
This work introduces a framework for estimating the graphlet count - the number of occurrences of a small subgraph motif (e.g. a wedge or a triangle) in the network.  ...  We outline three variants of lifted graphlet counts: the ordered, unordered, and shotgun estimators.  ...  This fact enables [19] to provide a local estimator of the stationary probability π (S).  ... 
arXiv:1802.08736v1 fatcat:lcv4h7mei5ecnh7bcuuvh5xzh4

Adaptive Shrinkage Estimation for Streaming Graphs [article]

Nesreen K. Ahmed, Nick Duffield
2020 arXiv   pre-print
In this work, we consider the fundamental problem of estimating the higher-order dependencies using adaptive sampling.  ...  We propose a novel adaptive, single-pass sampling framework and unbiased estimators for higher-order network analysis of large streaming networks.  ...  E[ S J,t ] = 1 and hence n i,t = J∈Hi,t S J,t is an unbiased estimator of the local subgraph count n i,t for all i ∈ K t .  ... 
arXiv:1908.01087v4 fatcat:nvtj6266mvfsxmpkzj7jlza4iq

Locating highly connected clusters in large networks with HyperLogLog counters [article]

Lotte Weedage, Nelly Litvak, Clara Stegehuis
2021 arXiv   pre-print
Our proposed approach adapts the HyperBall algorithm to localize regions with a high density of small subgraph patterns in large graphs in a memory-efficient manner.  ...  We use this method to evaluate three measures of subgraph connectivity: conductance, the number of triangles, and transitivity.  ...  The bottleneck of the HYPERBALL-type algorithms for local graphlet count is the initialisation that requires, for each node v, the exact count of the graphlets that involve v.  ... 
arXiv:2101.04610v1 fatcat:ybdwwab5nbfpbgtnepntdewtiu

Efficient estimation of graphlet frequency distributions in protein-protein interaction networks

N. Przulj, D. G. Corneil, I. Jurisica
2006 Bioinformatics  
Local structure of networks can be measured by the frequency distribution of graphlets, small connected non-isomorphic induced subgraphs.  ...  This measure of local structure has been used to show that high-confidence PPI networks have local structure of geometric random graphs.  ...  The research was supported by the Natural Sciences and Engineering Research Council of Canada, the Ontario Graduate Scholarship Program and IBM Canada. Conflict of Interest: none declared.  ... 
doi:10.1093/bioinformatics/btl030 pmid:16452112 fatcat:vf5ju3gypvdsnlgc2azzrhskoe
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