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A complexity dichotomy for hitting connected minors on bounded treewidth graphs: the chair and the banner draw the boundary [chapter]

Julien Baste, Ignasi Sau, Dimitrios M. Thilikos
2020 Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms  
contains a planar graph, which was critically needed in the algorithm presented in [5] in order to bound the treewidth of an F-minor-free graph.  ...  This article triggered several other (deterministic) techniques to obtain singleexponential algorithms for so-called connectivity problems on graphs of bounded treewidth, mostly based on algebraic tools  ...  However, in the proof this fact is only used to guarantee that the considered protrusion has treewidth bounded by a function depending only on F .  ... 
doi:10.1137/1.9781611975994.57 dblp:conf/soda/BasteST20 fatcat:ivoy6w7ky5hvlarn2flzspk7ay

Optimal Algorithms for Hitting (Topological) Minors on Graphs of Bounded Treewidth * †

Julien Baste, Ignasi Sau, Dimitrios Thilikos
unpublished
For a fixed collection of graphs F, the F-M-Deletion problem consists in, given a graph G and an integer k, decide whether there exists S  ...  For each such F, we assume w.l.o.g. that F is a topological minor antichain, we fix (H, B) to be an essential pair of F, and given an instance (G, k) of k × k P.  ...  Clique on (G, k) has a solution σ, then the σ-general H-solution is a solution of F-TM-Deletion on (G , ).  ... 
fatcat:3xucgqcyffafvfuhlgeww335wm

Hitting minors on bounded treewidth graphs. IV. An optimal algorithm [article]

Julien Baste, Ignasi Sau, Dimitrios M. Thilikos
2021 arXiv   pre-print
For a fixed finite collection of graphs F, the F-M-DELETION problem asks, given an n-vertex input graph G, for the minimum number of vertices that intersect all minor models in G of the graphs in F. by  ...  Courcelle Theorem, this problem can be solved in time f_ F(tw)· n^O(1), where tw is the treewidth of G, for some function f_ F depending on F In a recent series of articles, we have initiated the programme  ...  Hitting forbidden subgraphs in graphs of bounded treewidth.  ... 
arXiv:1907.04442v2 fatcat:35wobmemrjcgtfro65h6bo4xqe

Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable [article]

Petr A. Golovach, Giannos Stamoulis, Dimitrios M. Thilikos
2022 arXiv   pre-print
any of the graphs in ℱ as a topological minor.  ...  We prove that for every such ℱ, ℱ-TM-Deletion is fixed parameter tractable on planar graphs. Our algorithm runs in a 2^𝒪(k^2)· n^2 time or, alternatively in 2^𝒪(k)· n^4 time.  ...  Acknowledgements We wish to thank the anonymous reviewers for their comments and remarks that improved the presentation of this paper. Moreover, we are especially indebted to Fedor V.  ... 
arXiv:1907.02919v3 fatcat:ymswvnaay5bqlbzi4ydrwviqm4

Hitting Topological Minors is FPT [article]

Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Meirav Zehavi
2020 arXiv   pre-print
In the Topological Minor Deletion (TM-Deletion) problem input consists of an undirected graph G, a family of undirected graphs F and an integer k.  ...  For this case we improve upon the algorithm of Golovach et al. [SODA 2020] by designing an FPT algorithm with explicit dependence on k and h^.  ...  First we need an FPT algorithm for TM-Deletion on bounded treewidth graphs -this automatically yields such an algorithm for TMC on bounded treewidth graphs as well.  ... 
arXiv:1904.02944v2 fatcat:jqwnhemnerb4nn7blacvnt345u

Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable [chapter]

Petr A. Golovach, Giannos Stamoulis, Dimitrios M. Thilikos
2020 Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms  
any of the graphs in F as a topological minor.  ...  In particular, we provide an f (h, k) • n 2 algorithm where h is an upper bound to the vertices of the graphs in F.  ...  We define f 4 (k For simplicity, we use m = Acknowledgements We wish to thank the anonymous reviewers for their comments and remarks that improved the presentation of this paper.  ... 
doi:10.1137/1.9781611975994.56 dblp:conf/soda/GolovachST20 fatcat:ty6brsa6qjdq5peenloxtm6xwm

On Brambles, Grid-Like Minors, and Parameterized Intractability of Monadic Second-Order Logic [article]

Stephan Kreutzer, Siamak Tazari
2009 arXiv   pre-print
can be decided by a linear time algorithm on classes of graphs of bounded treewidth.  ...  Using our results from the first part of our work we establish a strong lower bound for tractability of MSO on classes of colored graphs.  ...  sets of edges (MSO 2 ) can be decided in linear time on any class of graphs of bounded treewidth [Cou90] .  ... 
arXiv:0907.3076v1 fatcat:ajfgzk6oqregpiwfrvvkec3viu

On Brambles, Grid-Like Minors, and Parameterized Intractability of Monadic Second-Order Logic [chapter]

Stephan Kreutzer, Siamak Tazari
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
Whereas much work has been done on designing, improving, and applying algorithms on graphs of bounded treewidth, not much is known on the side of lower bounds: what bound on the treewidth of a class of  ...  second-order logic (MSO), can be decided by a linear time algorithm on classes of graphs of bounded treewidth.  ...  sets of edges (MSO 2 ) can be decided in linear time on any class of graphs of bounded treewidth [7] .  ... 
doi:10.1137/1.9781611973075.30 dblp:conf/soda/KreutzerT10 fatcat:udgkaapsynhqlpbm5pg3vfqdxy

Lower Bounds on Dynamic Programming for Maximum Weight Independent Set [article]

Tuukka Korhonen
2021 arXiv   pre-print
It follows that treewidth characterizes optimal MWIS-circuits up to polynomials for all bounded degree graphs and H-minor-free graphs, and treedepth characterizes optimal MWIS-formulas up to polynomials  ...  We prove lower bounds on pure dynamic programming algorithms for maximum weight independent set (MWIS).  ...  In particular, H-topological-minor-free graphs generalize both bounded degree and H-minorfree graphs [33] , so proving a 2 Ω(w) lower bound for them seems like a natural next step.  ... 
arXiv:2102.06901v2 fatcat:wdrvmo2xqvd5vl3dhid4stwym4

A Complexity Dichotomy for Hitting Small Planar Minors Parameterized by Treewidth

Julien Baste, Ignasi Sau, Dimitrios M. Thilikos, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
For the version of the problem where H is forbidden as a topological minor, the case H = K 1,4 can be solved in time 2 Θ(tw) · n O(1) .  ...  For a fixed graph H, we are interested in the parameterized complexity of the following problem, called {H}-M-Deletion, parameterized by the treewidth tw of the input graph: given an nvertex graph G and  ...  Acknowledgements We would like to thank Eun Jung Kim and Édouard Bonnet for insightful discussions on the topic of this paper.  ... 
doi:10.4230/lipics.ipec.2018.2 dblp:conf/iwpec/BasteST18 fatcat:h2y3zxm4z5f2zmaevjhgoziufy

Parameterization Above a Multiplicative Guarantee

Fedor V. Fomin, Petr A. Golovach, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Meirav Zehavi, Michael Wagner
2020 Innovations in Theoretical Computer Science  
Here, g(I) is usually a lower bound (resp. upper bound) on the maximum (resp. minimum) size of a solution.  ...  In particular, we study the Long Cycle problem with a multiplicative parameterization above the girth g(I) of the input graph, and provide a parameterized algorithm for this problem.  ...  For any k ∈ N, any graph G of treewidth at least 60k 2 contains a k-prism as a topological minor. 2 In case the treewidth of the graph is low, we will be able to solve the problem by making use of the  ... 
doi:10.4230/lipics.itcs.2020.39 dblp:conf/innovations/FominGLP0Z20 fatcat:soqaonrddjeoljfyc6ce24s3ae

Bidimensionality and Kernels [article]

Fedor V. Fomin and Daniel Lokshtanov and Saket Saurabh and Dimitrios M. Thilikos
2020 arXiv   pre-print
Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs, J.  ...  Our results imply that a multitude of bidimensional problems g graph classes. For most of these problems no polynomial kernels on H-minor-free graphs were known prior to our work.  ...  In what follows, we prove that, for every (F, k) We consider some (F, k) ∈ F I × Z and we denote H = G 1 ⊕ F. Let S be an optimal solution of H. That is, |S| = OP T Π (H) and (H, S) |= ε.  ... 
arXiv:1606.05689v3 fatcat:472cpmaxlfailcqrtajs32sl5i

Hitting forbidden minors: Approximation and Kernelization [article]

Fedor V. Fomin, Daniel Lokshtanov, Neeldhara Misra, Geevarghese Philip, Saket Saurabh
2010 arXiv   pre-print
The generic kernelization algorithm is based on a non-trivial application of protrusion techniques, previously used only for problems on topological graph classes.  ...  ratio of O(^3/2 OPT), where OPT is the size of an optimal solution on general undirected graphs.  ...  The following well known result states that every optimization problem expressible in MSO has a linear time algorithm on graphs of bounded treewidth. Proposition 2 ( [4, 8, 14, 20, 22] ).  ... 
arXiv:1010.1365v1 fatcat:5abs6qzufja5dpj5gey52slyrq

Hitting forbidden minors: Approximation and Kernelization

Fedor V. Fomin, Daniel Lokshtanov, Neeldhara Misra, Geevarghese Philip, Saket Saurabh, Marc Herbstritt
2011 Symposium on Theoretical Aspects of Computer Science  
The generic kernelization algorithm is based on a non-trivial application of protrusion techniques, previously used only for problems on topological graph classes.  ...  We obtain a number of algorithmic results on the p-F -Deletion problem when F contains a planar graph.  ...  The following well known result states that every optimization problem expressible in MSO has a linear time algorithm on graphs of bounded treewidth. Proposition 2 ( [4, 7, 13, 16, 18] ).  ... 
doi:10.4230/lipics.stacs.2011.189 dblp:conf/stacs/FominLMPS11 fatcat:objrbhc4nbcndgaosbpvva2fhm

Losing Treewidth by Separating Subsets [article]

Anupam Gupta, Euiwoong Lee, Jason Li, Pasin Manurangsi, Michał Włodarczyk
2018 arXiv   pre-print
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  ...  We present their applications in bounded-degree graphs, and also give an APX-hardness result for the edge deletion problems.  ...  [FJP10] gave a 9approximation for Diamond Hitting Set, which is excluding the graph with two vertices and three parallel edges as a topological minor.  ... 
arXiv:1804.01366v2 fatcat:6oep65f2xvfvln3ldvb6cg5x6i
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