2018
DOI: 10.1145/3274662
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Practical Minimum Cut Algorithms

Abstract: The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both sequential and shared-memory parallel implementations of our algorithm. Extensive experiments on both real-world and generated… Show more

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Cited by 17 publications
(38 citation statements)
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References 178 publications
(501 reference statements)
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“…(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%
“…(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%
“…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%
“…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%