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Advanced Coarsening Schemes for Graph Partitioning

Ilya Safro, Peter Sanders, Christian Schulz
2015 ACM Journal of Experimental Algorithmics  
In this work, we focus on the coarsening phase, which is responsible for creating structures similar to the original but smaller graphs.  ...  running time and quality advantages of different coarsening schemes.  ...  Many opportunities remain to improve the coarsening schemes for graph partitioning.  ... 
doi:10.1145/2670338 fatcat:ndqaw74p6bbbrac43snfnt4tim

Advanced Coarsening Schemes for Graph Partitioning [chapter]

Ilya Safro, Peter Sanders, Christian Schulz
2012 Lecture Notes in Computer Science  
In this work, we focus on the coarsening phase, which is responsible for creating structures similar to the original but smaller graphs.  ...  running time and quality advantages of different coarsening schemes.  ...  Many opportunities remain to improve the coarsening schemes for graph partitioning.  ... 
doi:10.1007/978-3-642-30850-5_32 fatcat:6nlxm4cw6ja3fcwjokqx43xgz4

Advanced Coarsening Schemes for Graph Partitioning [article]

Ilya Safro, Peter Sanders, Christian Schulz
2012 arXiv   pre-print
In this work we focus on the coarsening phase, which is responsible for creating structurally similar to the original but smaller graphs.  ...  We compare different matching- and AMG-based coarsening schemes, experiment with the algebraic distance between nodes, and demonstrate computational results on several classes of graphs that emphasize  ...  Many opportunities remain to improve the coarsening schemes for graph partitioning.  ... 
arXiv:1201.6488v2 fatcat:mjtxhl6f2ndypgjbl7tmw2ftei

Advances in parallel partitioning, load balancing and matrix ordering for scientific computing

Erik G Boman, Umit V Catalyurek, Céedric Chevalier, Karen D Devine, Ilya Safro, Michael M Wolf
2009 Journal of Physics, Conference Series  
We summarize recent advances in partitioning, load balancing, and matrix ordering for scientific computing performed by members of the CSCAPES SciDAC institute.  ...  Acknowledgments Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U. S.  ...  Coarsening with a Weighted Aggregation Scheme Many common multilevel schemes for simple graphs are based on strict coarsening (Strict Aggregation SAG).  ... 
doi:10.1088/1742-6596/180/1/012008 fatcat:lite7s4ihvbwdbs7lrqypbyzve

Aggregative Coarsening for Multilevel Hypergraph Partitioning

Ruslan Shaydulin, Ilya Safro, Marc Herbstritt
2018 Symposium on Experimental and Efficient Algorithms  
Our coarsening schemes are inspired by the algebraic multigrid and stable matching approaches.  ...  Algorithms for many hypergraph problems, including partitioning, utilize multilevel frameworks to achieve a good trade-off between the performance and the quality of results.  ...  Hypergraph partitioning is less well-studied than graph partitioning [13] and there is a relative lack of advanced coarsening schemes compared to GP.  ... 
doi:10.4230/lipics.sea.2018.2 dblp:conf/wea/ShaydulinS18 fatcat:sjetiftqhrfnfhkwenrpxxi4we

Aggregative Coarsening for Multilevel Hypergraph Partitioning [article]

Ruslan Shaydulin, Ilya Safro
2018 arXiv   pre-print
Our coarsening schemes are inspired by the algebraic multigrid and stable matching approaches.  ...  Algorithms for many hypergraph problems, including partitioning, utilize multilevel frameworks to achieve a good trade-off between the performance and the quality of results.  ...  Hypergraph partitioning is less well-studied than graph partitioning [13] and there is a relative lack of advanced coarsening schemes compared to GP.  ... 
arXiv:1802.09610v2 fatcat:ne434ofxbbentjccqibcz5l32i

Solution of Large-Scale Supply Chain Models using Graph Sampling Coarsening [article]

Jiaze Ma, Victor M. Zavala
2021 arXiv   pre-print
We present a graph sampling and coarsening scheme (gSC) for computing lower and upper bounds for large-scale supply chain models.  ...  A graph coarsening (aggregation) scheme is used to compute an upper bound and to estimate the optimality gap of the approximate solution.  ...  We also derive a graph-coarsening scheme for computing an upper bound and to estimate the optimality gap of the approximate solution; here, we borrow coarsening schemes previously used in the literature  ... 
arXiv:2111.01249v1 fatcat:rpdk7a6xnbgfxhtze67i7k3r2q

Partitioning Complex Networks via Size-constrained Clustering [article]

Henning Meyerhenke and Peter Sanders and Christian Schulz
2014 arXiv   pre-print
During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm  ...  More precisely, our algorithm provides graph coarsening by iteratively contracting size-constrained clusterings that are computed using a label propagation algorithm.  ...  Iterated V-cycle Scheme in the matching-based coarsening case.  ... 
arXiv:1402.3281v2 fatcat:2ecuaiu2pnf7hpglaieo57g4ey

Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning

Ruslan Shaydulin, Ilya Safro, Jie Chen
2019 Multiscale Modeling & simulation  
The algebraic distance is a vertex distance measure that extends hyperedge weights for capturing the local connectivity of vertices which is critical for hypergraph coarsening schemes.  ...  The practical effectiveness of the proposed measure and corresponding coarsening scheme is demonstrated through extensive computational experiments on a diverse set of problems.  ...  The authors would like to thank Clemson University for generous allotment of computation time on Palmetto cluster and Palmetto support staff for technical assistance.  ... 
doi:10.1137/17m1152735 fatcat:qocfycgccjh4no7thhogrwrn2e

Balanced Coarsening for Multilevel Hypergraph Partitioning via Wasserstein Discrepancy [article]

Zhicheng Guo, Jiaxuan Zhao, Licheng Jiao, Xu Liu
2021 arXiv   pre-print
We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning.  ...  Our coarsening scheme fully takes into account the minimization of connectivity metric (objective function).  ...  In this paper, we propose some more advanced algorithms for the coarsening stage and the initial partitioning stage in k-way hypergraph partitioning task.  ... 
arXiv:2106.07501v1 fatcat:vwxsskx2kzdaxmchkk7c3kmkxm

Multilevel Refinement for Combinatorial Optimisation Problems

Chris Walshaw
2004 Annals of Operations Research  
In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make  ...  However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems.  ...  Kumar, 1998a) , commonly used for partitioning can only operate on weighted graphs and hence cannot be applied for the first coarsening step if the original graph is not weighted.  ... 
doi:10.1023/b:anor.0000039525.80601.15 fatcat:fxlninb3r5eapp5udbbdf5zbai

Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning [article]

Ruslan Shaydulin, Jie Chen, Ilya Safro
2019 arXiv   pre-print
The algebraic distance is a vertex distance measure that extends hyperedge weights for capturing the local connectivity of vertices which is critical for hypergraph coarsening schemes.  ...  The practical effectiveness of the proposed measure and corresponding coarsening scheme is demonstrated through extensive computational experiments on a diverse set of problems.  ...  The authors would like to thank Clemson University for generous allotment of computation time on Palmetto cluster and Palmetto support staff for technical assistance.  ... 
arXiv:1710.06552v4 fatcat:3lski3cqrneajnt6dc75tp6tey

A graphical heuristic for reduction and partitioning of large datasets for scalable supervised training

Sumedh Yadav, Mathis Bode
2019 Journal of Big Data  
Abstract A scalable graphical method is presented for selecting and partitioning datasets for the training phase of a classification task.  ...  A network design is also presented for a partitioning based distributed training formulation.  ...  Furthermore, a graph coarsening approach is presented to break the selected/reduced set into further partitions that are independently available for training, leading to an approximate learning scheme.  ... 
doi:10.1186/s40537-019-0259-3 fatcat:pfpu26egtfdydny5hp7wxpika4

Parallel Graph Partitioning for Complex Networks [article]

Henning Meyerhenke, Peter Sanders, Christian Schulz
2015 arXiv   pre-print
By introducing size constraints, label propagation becomes applicable for both the coarsening and the refinement phase of multilevel graph partitioning.  ...  For example, our algorithm can partition a web graph with 3.3 billion edges in less than sixteen seconds using 512 cores of a high performance cluster while producing a high quality partition -- none of  ...  ACKNOWLEDGEMENTS We would like to thank the Steinbuch Centre of Computing for giving us access to the Instituts Cluster II.  ... 
arXiv:1404.4797v3 fatcat:p7tgz4xej5cj3lghbx6qaltan4

Deep Multilevel Graph Partitioning [article]

Lars Gottesbüren, Tobias Heuer, Peter Sanders, Christian Schulz, Daniel Seemaier
2021 arXiv   pre-print
This is because most high-quality general-purpose graph partitioners are multilevel algorithms which perform graph coarsening to build a hierarchy of graphs, initial partitioning to compute an initial  ...  However, for large number of blocks, the smallest graph in the hierarchy that is used for initial partitioning still has to be large.  ...  Generic Deep MGP In this section, we present our first major contribution -a new partitioning scheme that we call Deep Multilevel Graph Partitioning.  ... 
arXiv:2105.02022v1 fatcat:zzqlj2thujcync7mllt3fxtoay
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