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Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization

Jiong Guo, Jens Gramm, Falk Hüffner, Rolf Niedermeier, Sebastian Wernicke
2006 Journal of computer and system sciences (Print)  
Here, m denotes the number of graph edges, k denotes the size of the feedback vertex set searched for, and c is a constant.  ...  As a further result, we present a fixed-parameter algorithm with runtime O(2 k · m 2 ) for the NP-complete EDGE BIPARTIZATION problem, which asks for at most k edges to remove from a graph to make it bipartite  ...  Acknowledgments The authors thank the anonymous referees of WADS 2005 for helpful and inspiring comments and an anonymous referee of the Journal of Computer and System Sciences for helping to improve the  ... 
doi:10.1016/j.jcss.2006.02.001 fatcat:aoxbedbjmnd2jged7hlbc7xmma

Improved Fixed-Parameter Algorithms for Two Feedback Set Problems [chapter]

Jiong Guo, Jens Gramm, Falk Hüffner, Rolf Niedermeier, Sebastian Wernicke
2005 Lecture Notes in Computer Science  
of the feedback vertex set searched for, and c is a constant.  ...  As a second result, we present a fixed-parameter algorithm for the NPcomplete Edge Bipartization problem with runtime O(2 k · m 2 ).  ...  The authors would like to thank the anonymous referees of WADS 2005 for helpful and inspiring comments.  ... 
doi:10.1007/11534273_15 fatcat:hxjgozqbdzg4vbpwxesls2riuy

Iterative Compression for Exactly Solving NP-Hard Minimization Problems [chapter]

Jiong Guo, Hannes Moser, Rolf Niedermeier
2009 Lecture Notes in Computer Science  
We describe several algorithmic results based on iterative compression and point out some challenges for future research.  ...  This technique has proven very useful for achieving a number of recent breakthroughs in the development of fixed-parameter algorithms for NP-hard minimization problems.  ...  Acknowledgement: We are grateful to Christian Komusiewicz, Matthias Müller-Hannemann, and Siavash Vahdati Daneshmand for constructive comments improving the presentation of this paper.  ... 
doi:10.1007/978-3-642-02094-0_4 fatcat:ley2ifkrxbcw7bhzrktb5ijawq

Techniques for Practical Fixed-Parameter Algorithms

F. Huffner, R. Niedermeier, S. Wernicke
2007 Computer journal  
The fixed-parameter approach is an algorithm design technique for solving combinatorially hard (mostly NP-hard) problems.  ...  For some of these problems, it can lead to algorithms that are both efficient and yet at the same time guaranteed to find optimal solutions.  ...  Being the only fixed-parameter algorithm known for EDGE BIPARTIZATION, this algorithm is similar to the iterative compression algorithm that Reed et al.  ... 
doi:10.1093/comjnl/bxm040 fatcat:jbffitiefzfexftg3lgl7xnsza

Compression via Matroids: A Randomized Polynomial Kernel for Odd Cycle Transversal [article]

Stefan Kratsch, Magnus Wahlström
2011 arXiv   pre-print
In a breakthrough result Reed, Smith, and Vetta (Operations Research Letters, 2004) gave a (4^kkmn) time algorithm for it, the first algorithm with polynomial runtime of uniform degree for every fixed  ...  For OCT, the matroid is built to allow us to simulate the computation of the iterative compression step of the algorithm of Reed, Smith, and Vetta, applied (for only one round) to an approximate odd cycle  ...  for Feedback Vertex Set and Odd Cycle Transversal.  ... 
arXiv:1107.3068v2 fatcat:7xivak7xhvbgnmpazcgr2kdvlq

Algorithm Engineering for Optimal Graph Bipartization

Falk Hüffner
2009 Journal of Graph Algorithms and Applications  
We examine exact algorithms for the NP-hard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite.  ...  Based on the "iterative compression" method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental results. The worst-case time complexity is improved.  ...  Acknowledgments The author is grateful to Jens Gramm (Tübingen) and Jiong Guo, Rolf Niedermeier, and Sebastian Wernicke (Jena) for many helpful suggestions.  ... 
doi:10.7155/jgaa.00177 fatcat:4lrmvfxhcndsfjtajfcql2hyme

Algorithm Engineering for Optimal Graph Bipartization [chapter]

Falk Hüffner
2005 Lecture Notes in Computer Science  
We examine exact algorithms for the NP-hard Graph Bipartization problem. The task is, given a graph, to find a minimum set of vertices to delete to make it bipartite.  ...  Based on the "iterative compression" method introduced by Reed, Smith, and Vetta in 2004, we present new algorithms and experimental results. The worst-case time complexity is improved.  ...  Acknowledgments The author is grateful to Jens Gramm (Tübingen) and Jiong Guo, Rolf Niedermeier, and Sebastian Wernicke (Jena) for many helpful suggestions. JGAA, 13(2) 77-98 (2009) 95  ... 
doi:10.1007/11427186_22 fatcat:qzxhojrswrf45ks4zntpoacnsm

Experimental Evaluation of Parameterized Algorithms for Feedback Vertex Set

Krzysztof Kiljan, Marcin Pilipczuk, Marc Herbstritt
2018 Symposium on Experimental and Efficient Algorithms  
In this paper we provide an exhaustive experimental evaluation of fixed-parameter and branching algorithms for Feedback Vertex Set.  ...  From the point of view of parameterized algorithms and fixed-parameter tractability, Feedback Vertex Set is one of the landmark problems: a long line of study resulted in multiple algorithmic approaches  ...  Conclusions We have conducted a thorough experimental evaluation of various parameterized algorithms for the Feedback Vertex Set problem, following the setup of Parameterized Algorithms and Computational  ... 
doi:10.4230/lipics.sea.2018.12 dblp:conf/wea/KiljanP18 fatcat:symgz3xuzfffzphp5jkzox3qwy

Simpler Parameterized Algorithm for OCT [chapter]

Daniel Lokshtanov, Saket Saurabh, Somnath Sikdar
2009 Lecture Notes in Computer Science  
We give a simple and intuitive fixed parameter tractable algorithm for the Odd Cycle Transversal problem, running in time O(3 k · k · |E| · |V |).  ...  Our algorithm is best viewed as a reinterpretation of the classical Iterative Compression algorithm for Odd Cycle Transversal by Reed, Smith and Vetta [8] .  ...  Fomin, Rolf Niedermeier, Venkatesh Raman and Frances Rosamond for helpful discussions and for suggesting to put this article in print.  ... 
doi:10.1007/978-3-642-10217-2_37 fatcat:sifiew6vt5gbhbpslmtflzv6ue

A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems [chapter]

Michael R. Fellows, Jiong Guo, Hannes Moser, Rolf Niedermeier
2009 Lecture Notes in Computer Science  
This class includes problems such as Vertex Cover (here the corresponding compression task is decidable in polynomial time) or Undirected Feedback Vertex Set (here the corresponding compression task is  ...  We consider a large class of vertex deletion problems on undirected graphs and show that, except for few cases which are polynomial-time solvable, the others are NP-complete.  ...  For instance, the fixed-parameter tractability results (using iterative compression) for Vertex Bipartization [17] or Undirected Feedback Vertex Set [3, 5, 8] leave open whether the respective Compression  ... 
doi:10.1007/978-3-642-03816-7_28 fatcat:3gifzkyfkbaw3gvaedx5cynmda

A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems

Michael R. Fellows, Jiong Guo, Hannes Moser, Rolf Niedermeier
2011 ACM Transactions on Computation Theory  
This class includes problems such as Vertex Cover (here the corresponding compression task is decidable in polynomial time) or Undirected Feedback Vertex Set (here the corresponding compression task is  ...  We consider a large class of vertex deletion problems on undirected graphs and show that, except for few cases which are polynomial-time solvable, the others are NP-complete.  ...  For instance, the fixed-parameter tractability results (using iterative compression) for Vertex Bipartization [17] or Undirected Feedback Vertex Set [3, 5, 8] leave open whether the respective Compression  ... 
doi:10.1145/1944857.1944860 fatcat:ci3bfpo4r5bulg3g4t4y2n2xly

A survey of parameterized algorithms and the complexity of edge modification [article]

Christophe Crespelle, Pål Grønås Drange, Fedor V. Fomin, Petr A. Golovach
2020 arXiv   pre-print
The survey provides an overview of the developing area of parameterized algorithms for graph modification problems.  ...  We concentrate on edge modification problems, where the task is to change a small number of adjacencies in a graph in order to satisfy some required property.  ...  We thank Marcin Pilipczuk, William Lochet, and Dekel Tsur for helpful comments. References  ... 
arXiv:2001.06867v2 fatcat:6ogysat6n5drpbxsvs63zjmega

Iterative compression and exact algorithms

Fedor V. Fomin, Serge Gaspers, Dieter Kratsch, Mathieu Liedloff, Saket Saurabh
2010 Theoretical Computer Science  
We exemplify our findings with algorithms for the Maximum Independent Set problem, a parameterized and a counting version of d-Hitting Set and the Maximum Induced Cluster Subgraph problem.  ...  Iterative Compression has recently led to a number of breakthroughs in parameterized complexity.  ...  The authors are grateful to an anonymous referee for many suggestions helping us to improve the presentation of the paper.  ... 
doi:10.1016/j.tcs.2009.11.012 fatcat:xgs4a57pcbhhnkqrmlg3l2eata

Linear Time Parameterized Algorithms via Skew-Symmetric Multicuts [article]

M. S. Ramanujan, Saket Saurabh
2013 arXiv   pre-print
Using our algorithm, we show that Almost 2-SAT has an algorithm with running time O(4^kk^4ℓ) and we obtain algorithms for Odd Cycle Transversal and Edge Bipartization which run in time O(4^kk^4(m+n)) and  ...  This gives the first fixed-parameter tractable algorithm for this problem answering a question posed in a paper by a superset of the authors [STACS, 2013].  ...  Using a known linear time parameter preserving reduction from Edge Bipartization to OCT, we also get a similar result for Edge Bipartization.  ... 
arXiv:1304.7505v1 fatcat:bzafkg6glzahxl2jy7pzsfxttu

Representative sets and irrelevant vertices: New tools for kernelization [article]

Stefan Kratsch, Magnus Wahlström
2012 arXiv   pre-print
For a directed graph G=(V,E) and sets S, T ⊆ V, let r be the size of a minimum (S,T)-vertex cut (which may intersect S and T).  ...  We can find a set Z ⊆ V of size O(|S|*|T|*r) which contains a minimum (A,B)-vertex cut for every A ⊆ S, B ⊆ T.  ...  The authors are grateful to Dániel Marx for comments on an early draft of the paper, and to Saket Saurabh for an early version of [32] .  ... 
arXiv:1111.2195v2 fatcat:ienvm4zagndaxhew246stssnka
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