Practical Minimum Cut Algorithms

Henzinger, Monika; Noe, Alexander; Schulz, Christian; Strash, Darren

doi:10.1145/3274662

Cited by 15 publications

(38 citation statements)

References 178 publications

(501 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(4)) and HeavyTriangle (2. (5)) are reductions that were originally used for the minimum cut problem [8,22,34]. We adapt them and transfer them to the minimum multiterminal cut problem.…”

Section: Local Contractionmentioning

confidence: 99%

Shared-Memory Branch-and-Reduce for Multiterminal Cuts

Henzinger

Noe

Schulz

2020

2020 Proceedings of the Twenty-Second Workshop on Algorithm Engineering and Experiments (ALENEX)

Self Cite

View full text Add to dashboard Cite

We introduce the fastest known exact algorithm for the multiterminal cut problem with k terminals. In particular, we engineer existing as well as new data reduction rules. We use the rules within a branch-and-reduce framework and to boost the performance of an ILP formulation. Our algorithms achieve improvements in running time of up to multiple orders of magnitudes over the ILP formulation without data reductions, which has been the de facto standard used by practitioners. This allows us to solve instances to optimality that are significantly larger than was previously possible.

show abstract

“…(4)) and HeavyTriangle (2. (5)) are reductions that were originally used for the minimum cut problem [8,22,34]. We adapt them and transfer them to the minimum multiterminal cut problem.…”

Section: Local Contractionmentioning

confidence: 99%

Shared-Memory Branch-and-Reduce for Multiterminal Cuts

Henzinger

Noe

Schulz

2020

2020 Proceedings of the Twenty-Second Workshop on Algorithm Engineering and Experiments (ALENEX)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Consequently, fixed-points of improving mappings, which amount to persistent variables, cannot be found. For the closely related (yet polynomial-time solvable) MIN-CUT problem, a family of persistency criteria were proposed in [32,17]. They directly translate to the MAX-CUT problem and we derive them as special cases in our study below.…”

Section: Related Workmentioning

confidence: 99%

“…In our work we show how the framework of improving mappings developed in [37] can be used to derive persistency criteria for combinatorial problems with more complicated constraint structures, such as the MULTICUT and MAX-CUT problem, once a class of mappings that act on feasible solutions is identified. Specifically, we show that the known MULTICUT persistency criteria from [29] and the persistency criteria from [17] (transferred to the MAX-CUT problem) can be derived in our theoretical framework. Moreover, we define more powerful criteria that can find significantly more persistent variables, as shown in the experimental Section 7, yet can be evaluated efficiently.…”

Section: Related Workmentioning

confidence: 99%

Combinatorial Persistency Criteria for Multicut and Max-Cut

Lange

Andres

Swoboda

2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

View full text Add to dashboard Cite

In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to verify them. The criteria that we derive are based on mappings that improve feasible multicuts, respectively cuts. Our elementary criteria can be checked enumeratively. The more advanced ones rely on fast algorithms for upper and lower bounds for the respective cut problems and max-flow techniques for auxiliary min-cut problems. Our methods can be used as a preprocessing technique for reducing problem sizes or for computing partial optimality guarantees for solutions output by heuristic solvers. We show the efficacy of our methods on instances of both problems from computer vision, biomedical image analysis and statistical physics.

show abstract

“…There has been a MPI implementation of this algorithm by Gianinazzi et al [9]. However, there have been no parallel implementations of the algorithms of Hao et al [12] and Nagamochi et al [24,25], which outperformed other exact algorithms by orders of magnitude [7,13,15], both in real-world and generated networks.…”

Section: Introductionmentioning

confidence: 99%

Shared-Memory Exact Minimum Cuts

Henzinger

Noe

Schulz

2019

2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS)

Self Cite

View full text Add to dashboard Cite

The minimum cut problem for an undirected edgeweighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.State-of-the-art algorithms like the algorithm of Padberg and Rinaldi or the algorithm of Nagamochi, Ono and Ibaraki identify edges that can be contracted to reduce the graph size such that at least one minimum cut is maintained in the contracted graph. Our algorithm achieves improvements in running time over these algorithms by a multitude of techniques. First, we use a recently developed fast and parallel inexact minimum cut algorithm to obtain a better bound for the problem. Then we use reductions that depend on this bound, to reduce the size of the graph much faster than previously possible. We use improved data structures to further improve the running time of our algorithm. Additionally, we parallelize the contraction routines of Nagamochi, Ono and Ibaraki. Overall, we arrive at a system that outperforms the fastest stateof-the-art solvers for the exact minimum cut problem significantly.

show abstract

Practical Minimum Cut Algorithms

Cited by 15 publications

References 178 publications

Shared-Memory Branch-and-Reduce for Multiterminal Cuts

Shared-Memory Branch-and-Reduce for Multiterminal Cuts

Combinatorial Persistency Criteria for Multicut and Max-Cut

Shared-Memory Exact Minimum Cuts

Contact Info

Product

Resources

About