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A deterministic polynomial kernel for Odd Cycle Transversal and Vertex Multiway Cut in planar graphs [article]

Bart M.P. Jansen and Marcin Pilipczuk and Erik Jan van Leeuwen
2018 arXiv   pre-print
We show that Odd Cycle Transversal and Vertex Multiway Cut admit deterministic polynomial kernels when restricted to planar graphs and parameterized by the solution size.  ...  We also show connections between Vertex Multiway Cut and the Vertex Planarization problem, where the existence of a polynomial kernel remains an important open problem.  ...  Among other results, the framework provided a polynomial kernel for Odd Cycle Transversal and for Multiway Cut with a constant number of terminals.  ... 
arXiv:1810.01136v2 fatcat:hxolfduonvha3mlnhw2xiirurm

A Deterministic Polynomial Kernel for Odd Cycle Transversal and Vertex Multiway Cut in Planar Graphs

Bart M. P. Jansen, Marcin Pilipczuk, Erik Jan Van Leeuwen, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
We show that Odd Cycle Transversal and Vertex Multiway Cut admit deterministic polynomial kernels when restricted to planar graphs and parameterized by the solution size.  ...  We also show connections between Vertex Multiway Cut and the Vertex Planarization problem, where the existence of a polynomial kernel remains an important open problem.  ...  Odd Cycle Transversal and Vertex Multiway Cut, when restricted to planar graphs and parameterized by the solution size, admit deterministic polynomial kernels. 39:3 Figure 1 When all terminals (blue  ... 
doi:10.4230/lipics.stacs.2019.39 dblp:conf/stacs/JansenPL19 fatcat:u7f6rz4dl5dudfwsarvwga6le4

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

Stefan Kratsch, Magnus Wahlström
2011 arXiv   pre-print
The Odd Cycle Transversal problem (OCT) asks whether a given graph can be made bipartite by deleting at most k of its vertices.  ...  Since then the existence of a polynomial kernel for OCT, i.e., a kernelization with size bounded polynomially in k, has turned into one of the main open questions in the study of kernelization.  ...  for Feedback Vertex Set and Odd Cycle Transversal.  ... 
arXiv:1107.3068v2 fatcat:7xivak7xhvbgnmpazcgr2kdvlq

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
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.  ...  The survey provides an overview of the developing area of parameterized algorithms for graph modification problems.  ...  We thank Marcin Pilipczuk, William Lochet, and Dekel Tsur for helpful comments. References  ... 
arXiv:2001.06867v2 fatcat:6ogysat6n5drpbxsvs63zjmega

Clique cover and graph separation: New incompressibility results [article]

Marek Cygan and Stefan Kratsch and Marcin Pilipczuk and Michał Pilipczuk and Magnus Wahlström
2011 arXiv   pre-print
The existence of a polynomial kernelization for EDGE CLIQUE COVER was a seasoned veteran in open problem sessions.  ...  algorithm that reduces the size of an instance to polynomial in the parameter: - EDGE CLIQUE COVER, parameterized by the number of cliques, - DIRECTED EDGE/VERTEX MULTIWAY CUT, parameterized by the size  ...  We would like to thank Jakub Onufry Wojtaszczyk for some early discussions on the kernelization of the graph separation problems.  ... 
arXiv:1111.0570v1 fatcat:lgwwp64nhjec3gucexjf4fg6ky

A Framework for Parameterized Subexponential Algorithms for Generalized Cycle Hitting Problems on Planar Graphs [article]

Dániel Marx, Pranabendu Misra, Daniel Neuen, Prafullkumar Tale
2021 arXiv   pre-print
In particular, we use or adapt known kernelization results to obtain 2^O(√(k)·polylog(k)) n^O(1) time (randomized) algorithms for Vertex Multiway Cut, Group Feedback Vertex Set, and Subset Feedback Vertex  ...  We show that there is an n^O(√(k)) time algorithm on planar graphs for any problem that can be formulated this way, which includes a large number of well-studied problems, for example, Odd Cycle Transversal  ...  Subset Feedback Vertex Set can be solved in randomized time 2 O( √ k) • n O (1) on planar graphs. Currently no polynomial kernel is known for Subset Odd Cycle Transversal.  ... 
arXiv:2110.15098v1 fatcat:nimpu577gnagrlrev4xzemzlde

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms [article]

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 arXiv   pre-print
We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.  ...  Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  However, the situation is different for the minimization problem, since VERTEX COVER admits a 2-approximation algorithm, while ODD CYCLE TRANSVERSAL [226] and PERFECT DELETION [227] are NP-hard to  ... 
arXiv:2006.04411v1 fatcat:hjgu7f3s7zbydkcnioq3qlzgza

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 Algorithms  
We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.  ...  Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  However, the situation is different for the minimization problem, since VERTEX COVER admits a 2-approximation algorithm, while ODD CYCLE TRANSVERSAL [245] and PERFECT DELETION [246] are NP-hard to  ... 
doi:10.3390/a13060146 fatcat:2u2vv3uksfguvj6473t2gsq42a

Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity

Michael R. Fellows, Bart M.P. Jansen, Frances Rosamond
2013 European journal of combinatorics (Print)  
polynomial kernels.  ...  We call for a new type of race in parameterized analysis, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or  ...  Cut and Odd Cycle Transversal, and work on weighted problems [6, 23, 27, 57, 76] .  ... 
doi:10.1016/j.ejc.2012.04.008 fatcat:uzjyjuxec5hvlcep3jsf3mcupu

Losing Treewidth by Separating Subsets [article]

Anupam Gupta, Euiwoong Lee, Jason Li, Pasin Manurangsi, Michał Włodarczyk
2018 arXiv   pre-print
as k-Treewidth Vertex Deletion and Planar-F Vertex Deletion.  ...  We consider the case where graphs in H have treewidth bounded by t, and give a general framework to obtain approximation algorithms for both vertex and edge-deletion settings from approximation algorithms  ...  chordless or odd cycles.  ... 
arXiv:1804.01366v2 fatcat:6oep65f2xvfvln3ldvb6cg5x6i

Covering Small Independent Sets and Separators with Applications to Parameterized Algorithms [chapter]

Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Roohani Sharma, Meirav Zehavi
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
Put together, our new tools yield new randomized fixed parameter tractable (FPT) algorithms for Stable s-t Separator, Stable Odd Cycle Transversal and Stable Multicut on general graphs, and for Stable  ...  most k, the probability that X is a subset of Y is at least The second is a new (deterministic) polynomial time graph sparsification procedure that given a graph G, a set T = {{s 1 , t 1 }, {s 2 , t 2  ...  This notion was used to derive randomized polynomial kernels for many problems, including Almost 2-SAT and Multiway Cut with Deletable Terminals.  ... 
doi:10.1137/1.9781611975031.177 dblp:conf/soda/LokshtanovP0SZ18 fatcat:y7p4g3ipcnh23iofsohggf23am

Cumulative index volumes 1–92

2000 Discrete Applied Mathematics  
Szekely, Minimum multiway cuts in trees 87 (l-3) (1998) 67-75 Ergincan, F.8. and D.A. Gregory, 125 Dutton, R.D., see T.W.  ...  Laskar and J. Pfaff, A linear algorithm for finding a minimum dominating set in a , B., A polynomial algorithm for constucting the clique graph of a line graph 15 (1986) 61-66 Hefner, K.A.S., K.F.  ... 
doi:10.1016/s0166-218x(00)00210-9 fatcat:vvomn3k7hbbmliptwaczxk6wi4

Preprocessing to Deal with Hard Problems

Eva-Maria Christiana Hols, Humboldt-Universität Zu Berlin, Humboldt-Universität Zu Berlin
2020
For Vertex Cover, we will unify known results for kernelizations when parameterized by the size of a deletion set to a specified graph class.  ...  Finally, we consider graph cut problems, especially the Subset Feedback Vertex Set problem. We show that this problem has a randomized polynomial kernelization when the parameter is the solution size.  ...  Now, we can use Theorem 12.11 to obtain a randomized polynomial kernel for Odd Cycle Transversal. Proof.  ... 
doi:10.18452/21377 fatcat:axxisxirirhojeai2hp257pk34

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  Next, we show that all minimal transversals of a shellable! hypergraph can be listed in polynomial time.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

Techniques combinatoires pour les algorithmes paramétrés et les noyaux, avec applications aux problèmes de multicoupe. Sciences et Techniques du Languedoc THÈSE

Jean Daligault
2013 unpublished
-ODD CYCLES TRANSVERSAL (removing k vertices to make a graph bipartite) is FPT [110] .  ...  (i + l, i + 1) for odd l, l 0 (i, i + l) and (i + l, i) for odd l, l < 0 The sets S i for odd i are a model of a K k in G 2k .  ...  We show that MULTICUT IN TREES admits a polynomial kernel, i.e. can be reduced to instances of size polynomial in k.  ... 
fatcat:niffvydnxjbgroiw2w6cejbhny
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