A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

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

2020
*
Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms
*

contains a planar

doi:10.1137/1.9781611975994.57
dblp:conf/soda/BasteST20
fatcat:ivoy6w7ky5hvlarn2flzspk7ay
*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 . ...##
###
Optimal Algorithms for Hitting (Topological) Minors on Graphs of Bounded Treewidth * †

unpublished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 , ). ...

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

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*. ...

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

2022
*
arXiv
*
pre-print

any

arXiv:1907.02919v3
fatcat:ymswvnaay5bqlbzi4ydrwviqm4
*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. ...##
###
Hitting Topological Minors is FPT
[article]

2020
*
arXiv
*
pre-print

In the

arXiv:1904.02944v2
fatcat:jqwnhemnerb4nn7blacvnt345u
*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. ...##
###
Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable
[chapter]

2020
*
Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms
*

any

doi:10.1137/1.9781611975994.56
dblp:conf/soda/GolovachST20
fatcat:ty6brsa6qjdq5peenloxtm6xwm
*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. ...##
###
On Brambles, Grid-Like Minors, and Parameterized Intractability of Monadic Second-Order Logic
[article]

2009
*
arXiv
*
pre-print

can be decided by a linear time

arXiv:0907.3076v1
fatcat:ajfgzk6oqregpiwfrvvkec3viu
*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] . ...##
###
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
*

Whereas much work has been done

doi:10.1137/1.9781611973075.30
dblp:conf/soda/KreutzerT10
fatcat:udgkaapsynhqlpbm5pg3vfqdxy
*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] . ...##
###
Lower Bounds on Dynamic Programming for Maximum Weight Independent Set
[article]

2021
*
arXiv
*
pre-print

It follows that

arXiv:2102.06901v2
fatcat:wdrvmo2xqvd5vl3dhid4stwym4
*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. ...##
###
A Complexity Dichotomy for Hitting Small Planar Minors Parameterized by Treewidth

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. ...

##
###
Parameterization Above a Multiplicative Guarantee

2020
*
Innovations in Theoretical Computer Science
*

Here, g(I) is usually a lower

doi:10.4230/lipics.itcs.2020.39
dblp:conf/innovations/FominGLP0Z20
fatcat:soqaonrddjeoljfyc6ce24s3ae
*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 ...##
###
Bidimensionality and Kernels
[article]

2020
*
arXiv
*
pre-print

Subexponential parameterized

arXiv:1606.05689v3
fatcat:472cpmaxlfailcqrtajs32sl5i
*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. ...##
###
Hitting forbidden minors: Approximation and Kernelization
[article]

2010
*
arXiv
*
pre-print

The generic kernelization

arXiv:1010.1365v1
fatcat:5abs6qzufja5dpj5gey52slyrq
*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] ). ...##
###
Hitting forbidden minors: Approximation and Kernelization

2011
*
Symposium on Theoretical Aspects of Computer Science
*

The generic kernelization

doi:10.4230/lipics.stacs.2011.189
dblp:conf/stacs/FominLMPS11
fatcat:objrbhc4nbcndgaosbpvva2fhm
*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] ). ...##
###
Losing Treewidth by Separating Subsets
[article]

2018
*
arXiv
*
pre-print

We consider the case where

arXiv:1804.01366v2
fatcat:6oep65f2xvfvln3ldvb6cg5x6i
*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*. ...
« Previous

*Showing results 1 — 15 out of 199 results*