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Finding All Global Minimum Cuts in Practice

Monika Henzinger, Alexander Noe, Christian Schulz, Darren Strash, Peter Sanders, Fabrizio Grandoni, Grzegorz Herman
2020 European Symposium on Algorithms  
We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs.  ...  In shared memory we are able to find all minimum cuts of graphs with up to billions of edges and millions of minimum cuts in a few minutes.  ...  We adapt the routines originally developed for the minimum cut problem so that they hold for 59:6 Finding All Global Minimum Cuts in Practice the problem of for finding all minimum cuts.  ... 
doi:10.4230/lipics.esa.2020.59 dblp:conf/esa/HenzingerN0S20 fatcat:mykbuoxpzzhdxfnj57ababklkq

Finding All Global Minimum Cuts In Practice [article]

Monika Henzinger, Alexander Noe, Christian Schulz, Darren Strash
2020 arXiv   pre-print
We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs.  ...  In shared memory we are able to find all minimum cuts of graphs with up to billions of edges and millions of minimum cuts in a few minutes.  ...  The problem of finding all minimum cuts is closely related to the (global) minimum cut problem, which aims to find some minimum cut in the graph.  ... 
arXiv:2002.06948v1 fatcat:t4v3g2h2yfgennbymgyfyfitmq

Capacity Scaling for Graph Cuts in Vision

Olivier Juan, Yuri Boykov
2007 2007 IEEE 11th International Conference on Computer Vision  
Unlike some earlier hierarchical methods addressing efficiency of graph cuts in imaging, e.g. [16], capacity scaling preserves global optimality of the solution.  ...  Capacity scaling is a hierarchical approach to graph representation that can improve theoretical complexity and practical efficiency of max-flow/min-cut algorithms.  ...  In both cases the global minimum is the same (a gray circle) and any max-flow/min-cut algorithm finds it.  ... 
doi:10.1109/iccv.2007.4408970 dblp:conf/iccv/JuanB07 fatcat:4aokzrvs3jfp3dlas2ieb3beze

Practical Fully Dynamic Minimum Cut Algorithms [article]

Monika Henzinger, Alexander Noe, Christian Schulz
2021 arXiv   pre-print
We present a practically efficient algorithm for maintaining a global minimum cut in large dynamic graphs under both edge insertions and deletions.  ...  The algorithm uses the theoretical foundation and combines it with efficient and finely-tuned implementations to give an algorithm that can maintain the global minimum cut of a graph with rapid update  ...  Recently, we developed an algorithm that efficiently computes all minimum cuts of very large graphs in practice [20] .  ... 
arXiv:2101.05033v1 fatcat:jdup5v7sdnd43cq3dubmjvjnlu

Algorithm Engineering for Cut Problems [article]

Alexander Noe
2021 arXiv   pre-print
All of these algorithms are efficient in practice and freely available for use.  ...  This work develops highly-efficient algorithms for the (global) minimum cut problem, the balanced graph partitioning problem and the multiterminal cut problem.  ...  “Finding All Global Minimum Cuts in Practice”.  ... 
arXiv:2108.04566v1 fatcat:4tpyybkhsvg6toiuxkvdvychqu

Graph-cut methods for grain boundary segmentation

Song Wang, Jarrell Waggoner, Jeff Simmons
2011 JOM: The Member Journal of TMS  
Finding the globally optimal labeling that minimizes this cost function is NP-hard. However, the minimum graph-cut algorithm can be used to obtain a locally optimal labeling effi ciently.  ...  Finding the globally optimal normalized cut is a computationally intractable NP-hard problem.  ... 
doi:10.1007/s11837-011-0111-5 fatcat:r5rfd2kbgfb5ndpqgt27zyhoji

On Detection of Bounded Global Predicates

I.-C. Wu
1998 Computer journal  
Groselj [7] proposed an interesting method to derive the global state with minimum cost, called the minimum global snapshot [7] , by reducing the problem to a maximum network flow (or minimum cut) problem  ...  In order to detect bounded global predicates, we can first derive the minimum and maximum global snapshots and then check if the minimum and maximum are out of the range.  ...  that of [12] , to find the minimum cut cost.  ... 
doi:10.1093/comjnl/41.4.231 fatcat:wpsdoykccfhl7iapqlszv3hy7u

Fast approximate energy minimization via graph cuts

Y. Boykov, O. Veksler, R. Zabih
1999 Proceedings of the Seventh IEEE International Conference on Computer Vision  
We present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves, namely expansion moves and swap moves.  ...  Our expansion algorithm finds a labeling within a known factor of the global minimum, while our swap algorithm handles more general energy functions.  ...  [20] showed how to find the global minimum, in this case, by a single graph cut computation.  ... 
doi:10.1109/iccv.1999.791245 dblp:conf/iccv/BoykovVZ99 fatcat:v6i6o2ql4fde7jaymrbrir4ila

Fast approximate energy minimization via graph cuts

Y. Boykov, O. Veksler, R. Zabih
2001 IEEE Transactions on Pattern Analysis and Machine Intelligence  
We present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves, namely expansion moves and swap moves.  ...  Our expansion algorithm finds a labeling within a known factor of the global minimum, while our swap algorithm handles more general energy functions.  ...  [20] showed how to find the global minimum, in this case, by a single graph cut computation.  ... 
doi:10.1109/34.969114 fatcat:omqk3upxireangpjcog3oeqzwy

A New Algorithm for Energy Minimization with Discontinuities [chapter]

Yuri Boykov, Olga Veksler, Ramin Zabih
1999 Lecture Notes in Computer Science  
We have developed a new approximation algorithm based on graph cuts. The solution it generates is guaranteed to be within a factor of 2 of the energy function's global minimum.  ...  In this paper, we consider a natural class of energy functions that permits discontinuities. Computing the exact minimum is NP-hard.  ...  In practice, annealing is inefficient partly because at each step it changes the value of a single pixel. Graph cuts can be used to find the global minimum of certain energy functions.  ... 
doi:10.1007/3-540-48432-9_15 fatcat:ungty4jq6jdtlfze2l6vo44svy

Efficient Global Minimization for the Multiphase Chan-Vese Model of Image Segmentation [chapter]

Egil Bae, Xue-Cheng Tai
2009 Lecture Notes in Computer Science  
We have also developed a method for minimizing nonsubmodular functions, that can produce global solutions in practice should the condition not be satisfied, which may happen for the L  ...  In this work, we develop an efficient and global minimization method for a discrete version of the level set representation of the Chan-Vese model with 4 regions (phases), based on graph cuts.  ...  Graph cut minimization We will show that the discrete problem (9) can be minimized globally by finding the minimum cut on a specially designed graph.  ... 
doi:10.1007/978-3-642-03641-5_3 fatcat:6thwgumvlnbdflvidsmscpau4y

Optimizing Binary MRFs via Extended Roof Duality

Carsten Rother, Vladimir Kolmogorov, Victor Lempitsky, Martin Szummer
2007 2007 IEEE Conference on Computer Vision and Pattern Recognition  
In comparison to existing techniques, such as graph cut, TRW, BP, ICM, and simulated annealing, we nearly always find a lower energy.  ...  For several applications we see that we are able to find the global minimum very efficiently, and considerably outperform the original roof duality approach.  ...  Acknowledgements We thank the anonymous reviewers for pointing out the recent work [5] , Gabriel Tavares for running some tests on our datasets and sharing the implementation of "probing" used in [5]  ... 
doi:10.1109/cvpr.2007.383203 dblp:conf/cvpr/RotherKLS07 fatcat:yj3dvdusmrfghh7vmvyb4qmcmq

Conformational space annealing and an off-lattice frustrated model protein

Seung-Yeon Kim, Sung Jong Lee, Jooyoung Lee
2003 Journal of Chemical Physics  
The CSA successfully located the global minimum of the 46-mer for all 100 independent runs.  ...  Once a SA run is trapped in one of these quasi-global-minima, it cannot be folded into the global minimum before crossing over the two large energy barriers, clearly demonstrating the reason for the poor  ...  INTRODUCTION Finding the global minimum of a given function, called the global optimization, is an important problem in various fields of science and engineering.  ... 
doi:10.1063/1.1616917 fatcat:jy72qel53jbz7eemnza4kvdjgi

A New Method for Locating the Global Optimum: Application of the Cutting Angle Method to Molecular Structure Prediction [chapter]

Kieran F. Lim, Gleb Beliakov, Lynn Batten
2003 Lecture Notes in Computer Science  
Many problems in chemistry depend on the ability to identify the global minimum or maximum of a function.  ...  CAM is a general method that can also be applied to other computational problems involving global minima, global maxima or finding the roots of nonlinear equations.  ...  The authors wish to acknowledge support from the Australian Partnership in Advanced Computing (APAC) (Merit scheme grant d88) and School of Information Technology, Deakin University (internal grant).  ... 
doi:10.1007/3-540-44864-0_108 fatcat:wzdhpahgnbbbxcsdcgvuessmxm

Robust localization methods for passivity enforcement of linear macromodels

Zohaib Mahmood, Alessandro Chinea, Giuseppe C. Calafiore, Stefano Grivet-Talocia, Luca Daniel
2013 2013 17th IEEE Workshop on Signal and Power Integrity  
In this paper we solve a non-smooth convex formulation for passivity enforcement of linear macromodels using robust localization based algorithms such as the ellipsoid and the cutting plane methods.  ...  We also provide a lower bound on the global minimum, that grows tighter at each iteration and hence guarantees δ − optimality of the computed solution.  ...  Figures 6 shows the convergence of the cutting plane method to global minimum for different initial hypercubes.It also plots the piecewise linear lower bound on the global minimum.  ... 
doi:10.1109/sapiw.2013.6558312 fatcat:cqsfhydy35bzlkalrkaakpdvea
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