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Hitting Topological Minors is FPT [article]

Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Meirav Zehavi
2020 arXiv   pre-print
The task is to determine whether G contains a set of vertices S of size at most k, such that the graph G∖ S obtained from G by removing the vertices of S, contains no graph from F as a topological minor  ...  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.  ...  Since H is a topological minor in H , to prove that H is also a topological minor in G , it is enough to prove that H is a topological minor in G .  ... 
arXiv:1904.02944v2 fatcat:jqwnhemnerb4nn7blacvnt345u

Reducing graph transversals via edge contractions [article]

Paloma T. Lima, Vinicius F. dos Santos, Ignasi Sau, Uéverton S. Souza
2021 arXiv   pre-print
We focus on graph invariants defined as the minimum size of a vertex set that hits all the occurrences of graphs in a collection H according to a fixed containment relation.  ...  In sharp contrast, we show that when π is the size of a minimum vertex cover, the problem is in XP parameterized by d.  ...  , or topological minor containment relations.  ... 
arXiv:2005.01460v2 fatcat:ieexjr6gv5ewvkgcqelgytsbf4

Reducing Graph Transversals via Edge Contractions

Paloma T. Lima, Vinicius F. dos Santos, Ignasi Sau, Uéverton S. Souza, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
We focus on graph parameters defined as the minimum size of a vertex set that hits all the occurrences of graphs in a collection ℋ according to a fixed containment relation.  ...  In sharp contrast, we show that when π is the size of a minimum vertex cover, the problem is in XP parameterized by d.  ...  subgraph, minor, or topological minor containment relations.  ... 
doi:10.4230/lipics.mfcs.2020.64 dblp:conf/mfcs/LimaSSS20 fatcat:cv5jvedilrd7fbholr5prt6w7u

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

Stephan Kreutzer, Siamak Tazari
2009 arXiv   pre-print
Recently, Grohe and Marx showed that there are graphs G, in which every bramble of order larger than the square root of the treewidth is of exponential size in |G|.  ...  We use this algorithm to construct grid-like minors, a replacement structure for grid-minors recently introduced by Reed and Wood, in polynomial time.  ...  H is a topological minor of G if a subdivision of H is a subgraph of G. A topological minor of G is also a minor of G but the reverse is not true in general.  ... 
arXiv:0907.3076v1 fatcat:ajfgzk6oqregpiwfrvvkec3viu

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
The conclusions of non-uniform FPT algorithms being somewhat unsatisfactory, we essentially prove that if H is hereditary, union-closed, CMSO-definable, and (a) the canonical equivalence relation (or any  ...  Here, the torso of a vertex set S in a graph G is the graph with vertex set S and an edge between two vertices u, v ∈ S if there is a path between u and v in G whose internal vertices all lie outside S  ...  [15] , for hitting topological minors. As our algorithm is recursive, at every step we want to ensure that the neighbors of connected components in G − X ′ lie in one leaf-to-root path.  ... 
arXiv:2104.09950v3 fatcat:2itpufur5neqzi5fhxj53dxqvy

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  
We use this algorithm to construct grid-like minors, a replacement structure for grid-minors recently introduced by Reed and Wood, in polynomial time.  ...  Using the gridlike minors, we introduce the notion of a perfect bramble and an algorithm to find one in polynomial time.  ...  If the K -minor is, in fact, a topological minor, we call the structure a topological grid-like minor of order .  ... 
doi:10.1137/1.9781611973075.30 dblp:conf/soda/KreutzerT10 fatcat:udgkaapsynhqlpbm5pg3vfqdxy

Adapting the Directed Grid Theorem into an FPT Algorithm [article]

Victor Campos, Raul Lopes, Ana Karolinna Maia, Ignasi Sau
2022 arXiv   pre-print
Namely, they showed that there is a function f(k) such that every digraph of directed tree-width at least f(k) contains a cylindrical grid of size k as a butterfly minor and stated that their proof can  ...  Towards this, our main technical contributions are two FPT algorithms with parameter k.  ...  Since we showed that this problem is FPT with parameter |T | (Theorem 3.5), we can compute hitting sets of B T in FPT time with parameter ord(B T ).  ... 
arXiv:2007.07738v2 fatcat:6y47msh25jgnrntrjh4tru66ke

A use case of Content Delivery Network raw logfile analysis [article]

Hoang-Loc La, Anh-Tu Ngoc Tran, Quang-Trai Le, Masato Yoshimi, Takuma Nakajima, Nam Thoai
2021 arXiv   pre-print
However, there is still a certain gap between theories in academia and current technologies in industry.  ...  The CDN infrastructure, which we will consider in this paper, is dedicated to FPT Corporation [15] . FPT is one of the largest ISP companies in Vietnam.  ...  The hit rate of top 3 ISPs, which contribute the majority of traffic, are approximately the same. Besides, average latency of FPT is also better than the remaining ISPs.  ... 
arXiv:2106.06721v2 fatcat:7s5qwkqgqzdhzhltamzyrqaucq

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.  ...  The way to think of ≤ minor is to think of G ≤ minor H as taking |G| many collections C i of connected vertices of H, and coalescing each collection C i to a single vertex, then H being topologically embeddable  ...  A consequence of that result is that any filter with a finite basis in the topological quasi-ordering has an FPT membership algorithm.  ... 
doi:10.1007/978-3-642-30891-8_9 fatcat:fpq3zvaccfcavaxomwkeh5tyby

Using self-organizing maps to accelerate similarity search

Fanny Bonachera, Gilles Marcou, Natalia Kireeva, Alexandre Varnek, Dragos Horvath
2012 Bioorganic & Medicinal Chemistry  
Fuzzy tricentric pharmacophore (FPT) and ISIDA substructure counts are herein explored examples.  ...  The main goal is to discover and validate SOMs of optimal quality with respect to this criterion.  ...  This is however a minor issue, merely causing some (potentially avoidable) time loss due to the undue computation of a dissimilarity score.  ... 
doi:10.1016/j.bmc.2012.04.024 pmid:22595424 fatcat:c4s6xedamvdhriyuvxawsk2r4u

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  
Parameterization above a guarantee is a successful paradigm in Parameterized Complexity.  ...  Here, g(I) is usually a lower bound (resp. upper bound) on the maximum (resp. minimum) size of a solution.  ...  That is, it is FPT.  ... 
doi:10.4230/lipics.itcs.2020.39 dblp:conf/innovations/FominGLP0Z20 fatcat:soqaonrddjeoljfyc6ce24s3ae

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

Petr A. Golovach, Giannos Stamoulis, Dimitrios M. Thilikos
2022 arXiv   pre-print
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.  ...  problem. (4) ≤ is the minor 3 relation: again p -P F ,≤ -deletion is FPT, for every F.  ... 
arXiv:1907.02919v3 fatcat:ymswvnaay5bqlbzi4ydrwviqm4

Hitting Forbidden Minors: Approximation and Kernelization

Fedor V. Fomin, Daniel Lokshtanov, Neeldhara Misra, Geevarghese Philip, Saket Saurabh
2016 SIAM Journal on Discrete Mathematics  
The generic kernelization algorithm is based on a non-trivial application of protrusion techniques, previously used only for problems on topological graph classes.  ...  minors.  ...  Observe that for every vertex v the set H v is also a θ c hitting set for G, that is, H v hits all minor-models of θ c in G. Consider the graph G \ H v .  ... 
doi:10.1137/140997889 fatcat:ibdw3u7a6vel3hfat3j5rjhjom

Planar Disjoint-Paths Completion [article]

Isolde Adler, Stavros G. Kolliopoulos, Dimitrios M. Thilikos
2015 arXiv   pre-print
This bound is a function of k, independent of the size of G. Second, we show that the problem is fixed-parameter tractable, in particular, it can be solved in time f(k)· n^2.  ...  We now prove that there is a vertex x ∈ V (G * ) such that if R is aρ-rooted topological minor of G * then R is aρ-rooted topological minor of G * \ {x}.  ...  . , λ} is bounded by a function of k it is enough to show how to check in FPT time whether, for i = 1, . . . , λ, R i τ is aρ irooted topological minor of G * φ(i) wereρ i = ρ i ∪ {(x i new , x * i new  ... 
arXiv:1511.04952v2 fatcat:lxi76f5rnzgrbbeuwtvksnswae

Planar Disjoint-Paths Completion

Isolde Adler, Stavros G. Kolliopoulos, Dimitrios M. Thilikos
2015 Algorithmica  
This bound is a function of k, independent of the size of G. Second, we show that the problem is fixed-parameter tractable, in particular, it can be solved in time f (k) · n 2 .  ...  We now prove that there is a vertex x ∈ V (G * ) such that if R is aρ-rooted topological minor of G * then R is aρ-rooted topological minor of G * \ {x}.  ...  . , λ} is bounded by a function of k it is enough to show how to check in FPT time whether, for i = 1, . . . , λ, R i τ is aρ irooted topological minor of G * φ(i) wereρ i = ρ i ∪ {(x i new , x * i new  ... 
doi:10.1007/s00453-015-0046-2 fatcat:ufznjk6n4baqfm5oxvyyuie2we
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