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Multi-Stage Graph Peeling Algorithm for Probabilistic Core Decomposition [article]

Yang Guo, Xuekui Zhang, Fatemeh Esfahani, Venkatesh Srinivasan, Alex Thomo, Li Xing
2021 arXiv   pre-print
Recently, Esfahani et al. presented a probabilistic core decomposition algorithm based on graph peeling and Central Limit Theorem (CLT) that is capable of handling very large graphs.  ...  To make the previous PA focus more on dense subgraphs, we propose a multi-stage graph peeling algorithm (M-PA) that has a two-stage data screening procedure added before the previous PA.  ...  CONCLUSION We presented a multi-stage probabilistic graph peeling algorithm (M-PA) for core decomposition.  ... 
arXiv:2108.06094v1 fatcat:nudfuz2hffefzn45kudmrnjnbq

The set of solutions of random XORSAT formulae

Morteza Ibrahimi, Yash Kanoria, Matt Kraning, Andrea Montanari
2015 The Annals of Applied Probability  
This model presents several structural similarities to other ensembles of constraint satisfaction problems, such as k-satisfiability (k-SAT), hypergraph bicoloring and graph coloring.  ...  In order to study such subgraphs, we establish novel local weak convergence results for them.  ...  We apply peeling to G * , thus obtaining the decomposition of V * into U * ∪ W * as described for the original graph G above.  ... 
doi:10.1214/14-aap1060 fatcat:lpifybua7jamtkqfujew6tysg4

Graph-XLL: a Graph Library for Extra Large Graph Analytics on a Single Machine

Jian Wu, Venkatesh Srinivasan, Alex Thomo
2019 2019 10th International Conference on Information, Intelligence, Systems and Applications (IISA)  
Although these libraries provide many off-the-shelf algorithms for users, the in-memory graph representation limits their scalability for computing on large graphs.  ...  Graph libraries containing already-implemented algorithms are highly desired since users can conveniently use the algorithms off-the-shelf to achieve fast analytics and prototyping, rather than implementing  ...  For example, the edge-peeling algorithm optimizes Cohen's very first k-truss decomposition algorithm [32] with improved time complexity.  ... 
doi:10.1109/iisa.2019.8900744 dblp:conf/iisa/WuST19 fatcat:zfqbpssaeje2bch6zyuvyxhrwm

Change Detection in Dynamic Attributed Networks [article]

Isuru Udayangani Hewapathirana
2020 arXiv   pre-print
We categorize these methods based on the levels of structure in the graph that are exploited to detect changes. These levels are vertices, edges, subgraphs, communities and the overall graph.  ...  Attaching these additional attribute data to the corresponding vertices and edges yields an attributed graph.  ...  Roger Jarquin from the School of Mathematics and Statistics, University of Canterbury, New Zealand, for providing insight and expertise that greatly assisted this work.  ... 
arXiv:2001.04734v1 fatcat:ohzwafwe5bfe5i4ox6uvlnn6au

The Set of Solutions of Random XORSAT Formulae [chapter]

Morteza Ibrahimi, Yashodhan Kanoria, Matt Kraning, Andrea Montanari
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
This model presents several structural similarities to other ensembles of constraint satisfaction problems, such as ksatisfiability (k-SAT), hypergraph bicoloring, and graph coloring.  ...  In order to study such subgraphs, we establish novel local weak convergence results for them.  ...  We apply peeling to G * , thus obtaining the decomposition of V * into U * ∪ W * as described for the original graph G above.  ... 
doi:10.1137/1.9781611973099.62 dblp:conf/soda/IbrahimiKKM12 fatcat:x5tndinzufhapjrz367hot772e

Recent Advances in Practical Data Reduction [article]

Faisal Abu-Khzam, Sebastian Lamm, Matthias Mnich, Alexander Noe, Christian Schulz, Darren Strash
2020 arXiv   pre-print
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems.  ...  This has resulted in an algorithmic toolbox that is by now well-established. However, these theoretical algorithmic ideas have received very little attention from the practical perspective.  ...  During later stages of a data reduction algorithm, local reductions may lead to very few graph changes.  ... 
arXiv:2012.12594v3 fatcat:vpsucno5cvgotovfiihkyyytba

Message Reduction in the LOCAL Model is a Free Lunch

Shimon Bitton, Yuval Emek, Taisuke Izumi, Shay Kutten
2019 Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing - PODC '19  
The crux of this approach is that the simulating algorithm executed in stage (2) runs for αt rounds and sends at most 2αt · |S| messages.  ...  In particular, the performance of the simulating algorithm does not depend on the number |E| of edges in the underlying graph G.  ...  Many existing distributed spanner algorithms have a node collect the topology of the graph up to a distance of some r from itself [9, 12] or employ more sophisticated bounded diameter graph decomposition  ... 
doi:10.1145/3293611.3331582 dblp:conf/podc/BittonEIK19 fatcat:mgyu2qmaovgmjnz7bm44ruuupi

Community Discovery in Dynamic Networks

Giulio Rossetti, Rémy Cazabet
2018 ACM Computing Surveys  
Acknowledgement We thank Jane Carlen for her feedback that helped us correct some errors in the description of some methods.  ...  Two-Stage approaches are then further divided into Core based, Union Graph based and Survival Graph based methods, corresponding to different solutions to solve the problem of graph matching.  ...  Legend: G: Graph, P: Partition, DC: Dynamic Community, C: Community several core-nodes for a single community.  ... 
doi:10.1145/3172867 fatcat:x6gcg42j3raklfr2f2y3ou5u44

Dressi: A Hardware-Agnostic Differentiable Renderer with Reactive Shader Packing and Soft Rasterization [article]

Yusuke Takimoto, Hiroyuki Sato, Hikari Takehara, Keishiro Uragaki, Takehiro Tawara, Xiao Liang, Kentaro Oku, Wataru Kishimoto, Bo Zheng
2022 arXiv   pre-print
The DR algorithms of Dressi are fully written in our Vulkan-based AD for DR, Dressi-AD, which supports all primitive operations for DR.  ...  Stage packing, our runtime optimization technique, can adapt hardware constraints and efficiently execute complex computational graphs of DR with reactive cache considering the render pass hierarchy of  ...  We thank Naoya Hirai and Chun Geng for the appearance of skin shading.  ... 
arXiv:2204.01386v1 fatcat:fnpyuev5svfrvnrv3tiw45yili

The mesoscopic geometry of sparse random maps [article]

Nicolas Curien and Igor Kortchemski and Cyril Marzouk
2021 arXiv   pre-print
Albeit different at first sight, these two models can be treated in a unified way using a probabilistic version of the classical core-kernel decomposition.  ...  In particular, we show that the number of edges of the core of such maps, obtained by iteratively removing degree 1 vertices, is concentrated around √(n s_n).  ...  We thank Thomas Budzinski for sharing early stages of his work [Bud ], Éric Fusy for the reference [BCR ] as well as Charles Bordenave and Bram Petri for the pointer to [Wor , Theorem . ].  ... 
arXiv:2112.10719v1 fatcat:w4d7yjvsnbaxrcg2i4xfnkwzte

Factor Graphs for Robot Perception

Frank Dellaert, Michael Kaess
2017 Foundations and Trends in Robotics  
We introduce factor graphs as an economical representation within which to formulate the different inference problems, setting the stage for the subsequent sections on practical methods to solve them.  ...  We provide insight into the graphs underlying robotics inference, and how their sparsity is affected by the implementation choices we make, crucial for achieving highly performant algorithms.  ...  The latter paper also developed the peeling algorithm, which is essentially variable elimination on an arbitrary graph.  ... 
doi:10.1561/2300000043 fatcat:flxlfe5aerg7ha4zasswzerj3e

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  the e cient solution of a multi-stage water resource system planning.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

A Tensor Approach to Learning Mixed Membership Community Models [article]

Anima Anandkumar, Rong Ge, Daniel Hsu, Sham M. Kakade
2013 arXiv   pre-print
In this paper, we remove this restriction, and provide guaranteed community detection for a family of probabilistic network models with overlapping communities, termed as the mixed membership Dirichlet  ...  We propose a unified approach to learning these models via a tensor spectral decomposition method.  ...  Acknowledgements We thank the JMLR Action Editor Nathan Srebro and the anonymous reviewers for comments which significantly improved this manuscript.  ... 
arXiv:1302.2684v4 fatcat:wkezvya5arc2noxahgnhtfb6yq

A Review of Intelligent Fault Diagnosis for High-Speed Trains: Qualitative Approaches

Chao Cheng, Jiuhe Wang, Hongtian Chen, Zhiwen Chen, Hao Luo, Pu Xie
2020 Entropy  
Another major focus of our research is to introduce the background of high-speed trains, like the composition of the core subsystems, system structure, etc., based on which it becomes convenient for researchers  ...  Furthermore, future research trends for qualitative IFD approaches are also presented.  ...  ., causes, symptoms, locations of faults), and its edges are used to describe probabilistic relationships among each graph node.  ... 
doi:10.3390/e23010001 pmid:33374991 pmcid:PMC7822053 fatcat:rimr2xaq45a7rafbfdde33nmam

Randomized Numerical Linear Algebra: Foundations Algorithms [article]

Per-Gunnar Martinsson, Joel Tropp
2021 arXiv   pre-print
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems.  ...  ; full rank-revealing factorizations; solvers for linear systems; and approximation of kernel matrices that arise in machine learning and in scientific computing.  ...  Modern computing architectures (GPUs, multi-core CPUs, massively distributed systems) are powerful, but this power can only be unleashed by algorithms that minimize data movement and that are designed  ... 
arXiv:2002.01387v3 fatcat:kaqg3j55hzf6lobdqenuakqr3i
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