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Deleting, Eliminating and Decomposing to Hereditary Classes Are All FPT-Equivalent [article]

Akanksha Agrawal, Lawqueen Kanesh, Daniel Lokshtanov, Fahad Panolan, M. S. Ramanujan, Saket Saurabh, Meirav Zehavi
2022 arXiv   pre-print
For a graph class H, the graph parameters elimination distance to H (denoted by ed_ H) [Bulian and Dawar, Algorithmica, 2016], and H-treewidth (denoted by tw_ H) [Eiben et al.  ...  by itself or any of the others is FPT-equivalent to the standard vertex-deletion (to H) problem.  ...  on at most α(k) + k nodes, 23:6 Elimination Distance to Topological-minor-free Graphs is FPT problem definition, shortly.  ... 
arXiv:2104.09950v3 fatcat:2itpufur5neqzi5fhxj53dxqvy

Elimination Distance to Bounded Degree on Planar Graphs

Alexander Lindermayr, Sebastian Siebertz, Alexandre Vigny, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
function f and constant c whether the elimination distance of G to the class of degree d graphs is at most k.  ...  We study the graph parameter elimination distance to bounded degree, which was introduced by Bulian and Dawar in their study of the parameterized complexity of the graph isomorphism problem.  ...  Computing elimination distance for K 5 -minor free graphs This section is devoted to the proof of our main result: Theorem 1.1. We fix an instance (G, k), where G is K 5 -minor-free.  ... 
doi:10.4230/lipics.mfcs.2020.65 dblp:conf/mfcs/LindermayrSV20 fatcat:q7l6fqaqujhj7kewuxyjrbzg6a

Vertex Deletion Parameterized by Elimination Distance and Even Less [article]

Bart M. P. Jansen, Jari J. H. de Kroon, Michał Włodarczyk
2022 arXiv   pre-print
This is applicable to any graph class H for which the corresponding vertex-deletion problem admits a constant-factor approximation algorithm or an FPT algorithm paramaterized by the solution size.  ...  They are related to graph decompositions in which subgraphs that belong to a target class H (e.g., bipartite or planar) are considered simple.  ...  While FPT algorithms to compute H-elimination distance for minor-closed graph classes H were known before [20] via an excluded-minor characterization (even to compute the exact distance), to the best  ... 
arXiv:2103.09715v4 fatcat:vv3kluwdtjhqdhaflntr6msvdi

Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

Eun Jung Kim, Alexander Langer, Christophe Paul, Felix Reidl, Peter Rossmanith, Ignasi Sau, Somnath Sikdar
2015 ACM Transactions on Algorithms  
H-topological-minor-free graphs.  ...  class of H-topological-minor-free graphs, for any fixed graph H.  ...  Our gratitude also goes to the anonymous reviewers for thorough comments that improved the presentation of the article.  ... 
doi:10.1145/2797140 fatcat:njyhhxg2q5fyvowl3uryuyr3jy

Elimination distance to bounded degree on planar graphs [article]

Alexander Lindermayr, Sebastian Siebertz, Alexandre Vigny
2021 arXiv   pre-print
function f and constant c whether the elimination distance of G to the class of degree d graphs is at most k.  ...  We study the graph parameter elimination distance to bounded degree, which was introduced by Bulian and Dawar in their study of the parameterized complexity of the graph isomorphism problem.  ...  We might end up performing Case 2.2 up to |G| many times before going to Case 1 or Case 2.1. Therefore, the overall complexity is f (k, d) • n c for a computable function f and constant c.  ... 
arXiv:2007.02413v2 fatcat:ethiwpaxjjhv7fcnhq7q3lj4ny

Linear Kernels and Single-Exponential Algorithms via Protrusion Decompositions [chapter]

Eun Jung Kim, Alexander Langer, Christophe Paul, Felix Reidl, Peter Rossmanith, Ignasi Sau, Somnath Sikdar
2013 Lecture Notes in Computer Science  
H-topological-minor-free graphs.  ...  class of H-topological-minor-free graphs, for any fixed graph H.  ...  Our gratitude also goes to the anonymous reviewers for thorough comments that improved the presentation of the article.  ... 
doi:10.1007/978-3-642-39206-1_52 fatcat:2gdnwhym6rawniwqgj2lh6xyta

A Basic Parameterized Complexity Primer [chapter]

Rod Downey
2012 Lecture Notes in Computer Science  
It is not intended as a complete survey of this very broad area in its current state; rather it is intended to give a flavour of the techniques used and the directions taken.  ...  Since many of the contributed articles revolve around the concept of parameterized complexity, it seems reasonable to give the reader a (short) primer to this area.  ...  For every fixed H there is a c H such that every H-minor-free graph or treewidth ≥ c H · n has an n-grid as a minor.  ... 
doi:10.1007/978-3-642-30891-8_9 fatcat:fpq3zvaccfcavaxomwkeh5tyby

Parameterized Distributed Complexity Theory: A logical approach [article]

Sebastian Siebertz, Alexandre Vigny
2021 arXiv   pre-print
The central notion of efficiency in parameterized complexity is fixed-parameter tractability and we define the distributed analogue Distributed-FPT (for Distributed in {Local, Congest, Congested-Clique  ...  The Distributed-WEFT-hierarchy is defined analogously to the W-hierarchy in parameterized complexity theory via reductions to the weighted circuit satisfiability problem, but it turns out that this definition  ...  graphs excluding a fixed (topological) minor.  ... 
arXiv:1903.00505v2 fatcat:uhhsg6hcrnf3lduyebj45bhl54

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree [chapter]

Jannis Bulian, Anuj Dawar
2014 Lecture Notes in Computer Science  
We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al.  ...  We generalise deletion distance to a measure we call elimination distance to triviality, based on elimination trees or tree-depth decompositions.  ...  excluded topological minor [10] .  ... 
doi:10.1007/978-3-319-13524-3_12 fatcat:elbyocaifvdfrdwxkhj7zdofmq

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

Jannis Bulian, Anuj Dawar
2015 Algorithmica  
We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al.  ...  We generalise deletion distance to a measure we call elimination distance to triviality, based on elimination trees or tree-depth decompositions.  ...  excluded topological minor [10] .  ... 
doi:10.1007/s00453-015-0045-3 fatcat:aojf733y7vap5hpms43uhazuwq

Phylogenetic incongruence through the lens of Monadic Second Order logic

Steven Kelk, Leo van Iersel, Celine Scornavacca, Mathias Weller
2016 Journal of Graph Algorithms and Applications  
The notion of treewidth, which is most famously associated with the celebrated Graph Minors project of Robertson and Seymour [24], has had a profound impact upon algorithm design.  ...  ℓ) · O(n) on graphs of treewidth t, where n is the number of vertices in the graph.  ...  We say that T | Y is the subtree of T induced by Y . In graph theory terms, T | Y is a label-preserving topological minor of T .  ... 
doi:10.7155/jgaa.00390 fatcat:ne7rpnylt5hhhlrz6acfk4c3sy

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)  
The aim of this article is to motivate and describe the parameter ecology program, which studies how different parameters contribute to the difficulty of classical problems.  ...  An extensive overview of recent advances on this front is presented for the Vertex Cover problem.  ...  parameterized by the deletion distance to constant treewidth (regardless of what the constant is), when the inputs graphs are H-minor-free for some H.  ... 
doi:10.1016/j.ejc.2012.04.008 fatcat:uzjyjuxec5hvlcep3jsf3mcupu

Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree [article]

Jannis Bulian, Anuj Dawar
2014 arXiv   pre-print
We establish that graph canonisation, and thus graph isomorphism, is FPT when parameterized by elimination distance to bounded degree, extending results of Bouland et al. (2012).  ...  We generalise deletion distance to a measure we call elimination distance to triviality, based on elimination trees or tree-depth decompositions.  ...  smallest excluded topological minor [9] .  ... 
arXiv:1406.4718v2 fatcat:ibwbqostf5cchan4wufjeytsba

Parameterized circuit complexity of model checking first-order logic on sparse structures [article]

Michał Pilipczuk, Sebastian Siebertz, Szymon Toruńczyk
2018 arXiv   pre-print
We prove that for every class C of graphs with effectively bounded expansion, given a first-order sentence φ and an n-element structure A whose Gaifman graph belongs to C, the question whether φ holds  ...  in A can be decided by a family of AC-circuits of size f(φ)· n^c and depth f(φ)+c n, where f is a computable function and c is a universal constant.  ...  The authors thank Thomas Zeume for discussions on dynamic FO in the context of sparse graphs, which inspired this work.  ... 
arXiv:1805.03488v1 fatcat:icwb4eheurdajldzypst2ylgc4

Phylogenetic incongruence through the lens of Monadic Second Order logic [article]

Steven Kelk, Leo van Iersel, Celine Scornavacca
2015 arXiv   pre-print
A crucial component of this work is the observation that many of these measures, when bounded, imply the existence of an 'agreement forest' of bounded size, which in turn implies that an auxiliary graph  ...  In doing so we wish to demonstrate the considerable potential of MSOL - machinery still largely unknown outside the algorithmic graph theory community - within phylogenetics.  ...  We say that T | Y is the subtree of T induced by Y . In graph theory terms, T | Y is a label-preserving topological minor of T .  ... 
arXiv:1503.00368v1 fatcat:ie42fw4m5nenrhjdmbeh56kqga
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