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Hitting Topological Minors is FPT
[article]

2020
*
arXiv
*
pre-print

The task

arXiv:1904.02944v2
fatcat:jqwnhemnerb4nn7blacvnt345u
*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 . ...##
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Reducing graph transversals via edge contractions
[article]

2021
*
arXiv
*
pre-print

We focus on graph invariants defined as the minimum size of a vertex set that

arXiv:2005.01460v2
fatcat:ieexjr6gv5ewvkgcqelgytsbf4
*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. ...##
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Reducing Graph Transversals via Edge Contractions

2020
*
International Symposium on Mathematical Foundations of Computer Science
*

We focus on graph parameters defined as the minimum size of a vertex set that

doi:10.4230/lipics.mfcs.2020.64
dblp:conf/mfcs/LimaSSS20
fatcat:cv5jvedilrd7fbholr5prt6w7u
*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. ...##
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On Brambles, Grid-Like Minors, and Parameterized Intractability of Monadic Second-Order Logic
[article]

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

arXiv:0907.3076v1
fatcat:ajfgzk6oqregpiwfrvvkec3viu
*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. ...##
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Deleting, Eliminating and Decomposing to Hereditary Classes Are All FPT-Equivalent
[article]

2022
*
arXiv
*
pre-print

The conclusions of non-uniform

arXiv:2104.09950v3
fatcat:2itpufur5neqzi5fhxj53dxqvy
*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. ...##
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On Brambles, Grid-Like Minors, and Parameterized Intractability of Monadic Second-Order Logic
[chapter]

2010
*
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms
*

We use this algorithm to construct grid-like

doi:10.1137/1.9781611973075.30
dblp:conf/soda/KreutzerT10
fatcat:udgkaapsynhqlpbm5pg3vfqdxy
*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 . ...##
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Adapting the Directed Grid Theorem into an FPT Algorithm
[article]

2022
*
arXiv
*
pre-print

Namely, they showed that there

arXiv:2007.07738v2
fatcat:6y47msh25jgnrntrjh4tru66ke
*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 ). ...##
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A use case of Content Delivery Network raw logfile analysis
[article]

2021
*
arXiv
*
pre-print

However, there

arXiv:2106.06721v2
fatcat:7s5qwkqgqzdhzhltamzyrqaucq
*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. ...##
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A Basic Parameterized Complexity Primer
[chapter]

2012
*
Lecture Notes in Computer Science
*

It

doi:10.1007/978-3-642-30891-8_9
fatcat:fpq3zvaccfcavaxomwkeh5tyby
*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. ...##
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Using self-organizing maps to accelerate similarity search

2012
*
Bioorganic & Medicinal Chemistry
*

Fuzzy tricentric pharmacophore (

doi:10.1016/j.bmc.2012.04.024
pmid:22595424
fatcat:c4s6xedamvdhriyuvxawsk2r4u
*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. ...##
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Parameterization Above a Multiplicative Guarantee

2020
*
Innovations in Theoretical Computer Science
*

Parameterization above a guarantee

doi:10.4230/lipics.itcs.2020.39
dblp:conf/innovations/FominGLP0Z20
fatcat:soqaonrddjeoljfyc6ce24s3ae
*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*. ...##
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Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable
[article]

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. ...

##
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Hitting Forbidden Minors: Approximation and Kernelization

2016
*
SIAM Journal on Discrete Mathematics
*

The generic kernelization algorithm

doi:10.1137/140997889
fatcat:ibdw3u7a6vel3hfat3j5rjhjom
*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 . ...##
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Planar Disjoint-Paths Completion
[article]

2015
*
arXiv
*
pre-print

This bound

arXiv:1511.04952v2
fatcat:lxi76f5rnzgrbbeuwtvksnswae
*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 ...##
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Planar Disjoint-Paths Completion

2015
*
Algorithmica
*

This bound

doi:10.1007/s00453-015-0046-2
fatcat:ufznjk6n4baqfm5oxvyyuie2we
*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 ...
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