Max-Cut Above Spanning Tree is Fixed-Parameter Tractable

Madathil, Jayakrishnan; Saurabh, Saket; Zehavi, Meirav

doi:10.1007/978-3-319-90530-3_21

Cited by 5 publications

(7 citation statements)

References 8 publications

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“…Several studies have been made in the direction of providing fixed-parameter algorithms for the Max Cut problem [10,11,17,29]. Among these, a fair amount of kernelization rules have been introduced with the goal of effectively reducing Max Cut instances [10,11,17,29,30,18]. Those reductions typically have some constraints on the subgraphs, like being clique forests or clique-cycle forest.…”

Section: Related Workmentioning

confidence: 99%

“…Those reductions typically have some constraints on the subgraphs, like being clique forests or clique-cycle forest. Later, we propose a new set of reductions that does not need this property and cover most of the known reductions [11,17,29,18]. There are other reductions rules that are fairly simplistic and focus on very narrow cases [30].…”

Section: Related Workmentioning

confidence: 99%

“…Spanning Tree Bound. Another approach is based on utilizing the spanning forest of a graph [29]. For a given k ∈ N 0 , a Max Cut of size |V | − 1 + k is searched for.…”

Section: Related Workmentioning

confidence: 99%

“…The main feature of our new rules is that they do not depend on the computation of a clique-forest to determine if they can be applied. Furthermore, our new rules subsume almost all rules from previous works [10,11,17,29,18] with the exception of Reduction Rules 10 and 11 by Crowston et al [10]. We provide details in [19].…”

Section: New Data Reduction Rulesmentioning

confidence: 99%

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Engineering Kernelization for Maximum Cut

Ferizovic¹,

Hespe²,

Lamm³

et al. 2020

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

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Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut problem, kernelization algorithms are theoretically highly efficient for various parameterizations. However, the efficacy of these reduction rules in practice-to aid solving highly challenging benchmark instances to optimality-remains entirely unexplored.We engineer a new suite of efficient data reduction rules that subsume most of the previously published rules, and demonstrate their significant impact on benchmark data sets, including synthetic instances, and data sets from the VLSI and image segmentation application domains. Our experiments reveal that current state-of-the-art solvers can be sped up by up to multiple orders of magnitude when combined with our data reduction rules. On social and biological networks in particular, kernelization enables us to solve four instances that were previously unsolved in a ten-hour time limit with state-of-the-art solvers; three of these instances are now solved in less than two seconds.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…Spanning Tree Bound. Another approach is based on utilizing the spanning forest of a graph [29]. For a given k ∈ N 0 , a Max Cut of size |V | − 1 + k is searched for.…”

Section: Related Workmentioning

confidence: 99%

Section: New Data Reduction Rulesmentioning

confidence: 99%

See 2 more Smart Citations

Engineering Kernelization for Maximum Cut

Ferizovic¹,

Hespe²,

Lamm³

et al. 2020

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

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show abstract

“…This is one of the 21 problems shown to be NP-hard by Karp's seminal work [12]. To overcome this intractability, numerous researches have been done from the viewpoints of approximation algorithms [8,13,11,25], exponential-time exact algorithms [7,26], and fixed-parameter algorithms [3,16,17,22]. There are several graph classes for which the Max-Cut problem admits polynomial time algorithms [1,9].…”

Section: Introductionmentioning

confidence: 99%

An Improved Fixed-Parameter Algorithm for Max-Cut Parameterized by Crossing Number

Kobayashi

Miyazaki

et al. 2019

Lecture Notes in Computer Science

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The Max-Cut problem is known to be NP-hard on general graphs, while it can be solved in polynomial time on planar graphs. In this paper, we present a fixed-parameter tractable algorithm for the problem on "almost" planar graphs: Given an n-vertex graph and its drawing with k crossings, our algorithm runs in time O(2 k (n + k) 3/2 log(n + k)). Previously, Dahn, Kriege and Mutzel (IWOCA 2018) obtained an algorithm that, given an n-vertex graph and its 1-planar drawing with k crossings, runs in time O(3 k n 3/2 log n). Our result simultaneously improves the running time and removes the 1-planarity restriction.

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Upper and Lower Bounds for Different Parameterizations of (n,3)-MAXSAT

Belova

Bliznets

2018

Combinatorial Optimization and Applications

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Max-Cut Above Spanning Tree is Fixed-Parameter Tractable

Cited by 5 publications

References 8 publications

Engineering Kernelization for Maximum Cut

Engineering Kernelization for Maximum Cut

An Improved Fixed-Parameter Algorithm for Max-Cut Parameterized by Crossing Number

Upper and Lower Bounds for Different Parameterizations of (n,3)-MAXSAT

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