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A Simple and Strongly-Local Flow-Based Method for Cut Improvement [article]

Nate Veldt, David F. Gleich, Michael W. Mahoney
2016 arXiv   pre-print
This method solves the same objective as existing strongly-local flow-based methods, but it enables a simple implementation.  ...  We introduce and analyze a new method for locally-biased graph-based learning called SimpleLocal, which finds good conductance cuts near a set of seed vertices.  ...  In comparison with Improve, our method is strongly-local and practically scalable (given a max-flow solver for the local graphs).  ... 
arXiv:1605.08490v1 fatcat:4gb43tgz3rgtdboru7skjbnhfe

HyperSF: Spectral Hypergraph Coarsening via Flow-based Local Clustering [article]

Ali Aghdaei, Zhiqiang Zhao, Zhuo Feng
2021 arXiv   pre-print
Our approach leverages a recent strongly-local max-flow-based clustering algorithm for detecting the sets of hypergraph vertices that minimize ratio cut.  ...  To further improve the algorithm efficiency, we propose a divide-and-conquer scheme by leveraging spectral clustering of the bipartite graphs corresponding to the original hypergraphs.  ...  ACKNOWLEDGMENT This work is supported in part by the National Science Foundation under Grants CCF-2041519 (CAREER), CCF-2021309 (SHF), and CCF-2011412 (SHF).  ... 
arXiv:2108.07901v3 fatcat:nd74hogturfubmlkubln543jai

An Optimization Approach to Locally-Biased Graph Algorithms

Kimon Fountoulakis, David F. Gleich, Michael W. Mahoney
2017 Proceedings of the IEEE  
method and create a strongly local flow based method.  ...  Weakly-and-Strongly local spectral methods There are spectral analogues for each of the three flow-based constructions on the augmented graph.  ... 
doi:10.1109/jproc.2016.2637349 fatcat:5wunqhfstzfsfgljle56r4rhp4

Flow-Based Local Graph Clustering with Better Seed Set Inclusion [article]

Nate Veldt and Christine Klymko and David Gleich
2019 arXiv   pre-print
Flow-based methods for local graph clustering have received significant recent attention for their theoretical cut improvement and runtime guarantees.  ...  In this work we present two improvements for using flow-based methods in real-world semi-supervised clustering problems.  ...  SimpleLocal: Our previous strongly-local flow-based method which optimizes the localized conductance objective (1) for a seed set R and locality parameter ε.  ... 
arXiv:1811.12280v2 fatcat:qwfpsauegvfmbkp2ikhq3vr5ym

An optimization approach to locally-biased graph algorithms [article]

Kimon Fountoulakis, David Gleich, Michael Mahoney
2016 arXiv   pre-print
We provide a review and overview of this work, highlighting commonalities between seemingly-different approaches, and highlighting promising directions for future work.  ...  In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph algorithm; but more interesting are locally-biased graph algorithms that compute answers  ...  due to Orecchia and Zhu [56] sought to address the weak-locality of the Flow-Improve method and create a strongly local flow based method.  ... 
arXiv:1607.04940v3 fatcat:7jifluhe3zgjdcfyfpiq4tt6ya

Page 326 of Mathematical Reviews Vol. 57, Issue 1 [page]

1979 Mathematical Reviews  
Basically, the method generates “strongly feasible” bases from ordinary feasible bases by a simple graph- theoretic rule.  ...  The authors generalize the min-cut equals max-flow theorem for a finite network to an infinite network. The results are based on the previous works of H. Flanders [IEEE Trans.  ... 

Flow-based Algorithms for Improving Clusters: A Unifying Framework, Software, and Performance [article]

K. Fountoulakis, M. Liu, D. F. Gleich, M. W. Mahoney
2022 arXiv   pre-print
Many such cluster improvement algorithms are flow-based methods, by which we mean that operationally they require the solution of a sequence of maximum flow problems on a (typically implicitly) modified  ...  These cluster improvement algorithms are powerful, both in theory and in practice, but they have not been widely adopted for problems such as community detection, local graph clustering, semi-supervised  ...  of flow algorithms, and finally Kent Quanrud for many helpful pointers.  ... 
arXiv:2004.09608v3 fatcat:f3ma3k4dsbgjherlsie2jtzc34

Fast Local Flow-based Method using Parallel Multi-core CPUs Architecture

Rashed Salem, Menoufia University, Wafaa Abdel-Moneim, Mohamed Hassan, Zagazig University, Zagazig University
2021 International Journal of Intelligent Engineering and Systems  
From the experiments, the proposed method improves the runtimes with 75.43% using 4-cores and 81.01% when using 8-cores over the sequential single core.  ...  Traditional methods of clustering are not suitable to tackle the problem of clustering large graphs because the computation is very costly, which is solved by local graph clustering using a given vertex  ...  Author Contributions The entire work of conceptualization, formal analysis, validation, implementation, writing, editing and modification of manuscript were done by Rashed Salem and Wafaa Abdel-Moneim  ... 
doi:10.22266/ijies2021.0831.01 fatcat:aekbnk5ssrakbacien6jq3gzke

Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning [article]

Meng Liu, Nate Veldt, Haoyu Song, Pan Li, David F. Gleich
2021 arXiv   pre-print
Specifically, it runs in few seconds for hypergraphs with a few million hyperedges compared with minutes for flow-based technique.  ...  We prove that, for graphs with fixed maximum hyperedge size, this method is strongly local, meaning that its runtime only depends on the size of the output instead of the size of the hypergraph and is  ...  (ii) flow [33] , which is the maxflow-mincut based local method designed for hypergraphs.  ... 
arXiv:2011.07752v2 fatcat:fek5cjwoonbwpnbud7atwpw4nu

Capacity Scaling for Graph Cuts in Vision

Olivier Juan, Yuri Boykov
2007 2007 IEEE 11th International Conference on Computer Vision  
Capacity scaling is a hierarchical approach to graph representation that can improve theoretical complexity and practical efficiency of max-flow/min-cut algorithms.  ...  While [3] is the fastest method for many applications in vision, capacity scaling gives several folds speed-ups for problems with large number of local minima.  ...  For example, it can be applied to more recent methods based on pre-flows (e.g. push-relabel algorithm of Goldberg and Tarjan) and on pseudo-flows (Hochbaum [9] ).  ... 
doi:10.1109/iccv.2007.4408970 dblp:conf/iccv/JuanB07 fatcat:4aokzrvs3jfp3dlas2ieb3beze

Page 7478 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
As applications to Lawrence type integer programming problems, we analyze the number of dual feasible bases for minimum cost flow problems and for multidimensional transportation problems of type2x---x2xMxN  ...  “We show that the separation problem for BC-cuts is strongly NP-hard in general, but polynomially solvable in certain special cases.  ... 

Engineering Multilevel Graph Partitioning Algorithms [article]

Peter Sanders, Christian Schulz
2011 arXiv   pre-print
Local improvement algorithms are based max-flow min-cut computations and more localized FM searches.  ...  We present a multi-level graph partitioning algorithm using novel local improvement algorithms and global search strategies transferred from the multi-grid community.  ...  Acknowledgements We would like to thank Vitaly Osipov for supplying data for KaSPar and Henning Meyerhenke for providing a DiBaP-full executable.  ... 
arXiv:1012.0006v3 fatcat:7a4cq7jjhvbfnc6bifuqjpfeea

p-Norm Flow Diffusion for Local Graph Clustering [article]

Kimon Fountoulakis, Di Wang, Shenghao Yang
2020 arXiv   pre-print
methods, and a smooth transition for general p values in between.  ...  In this work, we draw inspiration from both fields and propose a family of convex optimization formulations based on the idea of diffusion with p-norm network flow for p∈ (1,∞).  ...  Some examples include the flow-improve method [4] , the local flow-improve method [31] and the capacity releasing diffusion [39] .  ... 
arXiv:2005.09810v3 fatcat:ulsu5io6j5gmjijb463b6w5ixe

Self-organization and identification of Web communities

G.W. Flake, S. Lawrence, C.L. Giles, F.M. Coetzee
2002 Computer  
Applications include improved search engines, content filtering, and objective analysis of relationships within and between communities on the web.  ...  Despite the decentralized and unorganized nature of the web, we show that the web self-organizes such that communities of highly related pages can be efficiently identified based purely on connectivity  ...  Acknowledgments We thank Inktomi for the random URL data.  ... 
doi:10.1109/2.989932 fatcat:wgcx3hrof5hp7mnnzoueqvgqgy

Efficient maximum flow algorithms

Andrew V. Goldberg, Robert E. Tarjan
2014 Communications of the ACM  
Before formally defining the maximum flow and the minimum cut problems, we give a simple example of each problem: For the maximum flow example, suppose we have a graph that represents an oil pipeline network  ...  As the name implies, the algorithm is based on blocking flows. No comparable bound for the push-relabel method is known. This fact revives the theoretical importance of the blocking flow method.  ...  Although the running time of this algorithm (O(n 2 m log U) ) is not competitive with that of the best algorithms, the method is simple and extends to give a very simple and practical algorithm for a parametric  ... 
doi:10.1145/2628036 fatcat:chwxrnxvnfdfxeekdiyjzz2toi
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