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Fixed-parameter Tractable Distances to Sparse Graph Classes
[article]

2015
*
arXiv
*
pre-print

*graph*G

*to*C is

*fixed*-

*parameter*

*tractable*. ... We show that for various

*classes*C of

*sparse*

*graphs*, and several measures of

*distance*

*to*such

*classes*(such as edit

*distance*and elimination

*distance*), the problem of determining the

*distance*of a given ... In this paper we consider the

*fixed*-

*parameter*

*tractability*of a variety of different notions of

*distance*

*to*various different

*classes*C of

*sparse*

*graphs*. ...

##
###
Fixed-Parameter Tractable Distances to Sparse Graph Classes

2016
*
Algorithmica
*

*graph*G

*to*C is

*fixed*-

*parameter*

*tractable*. ... We show that for various

*classes*C of

*sparse*

*graphs*, and several measures of

*distance*

*to*such

*classes*(such as edit

*distance*and elimination

*distance*), the problem of determining the

*distance*of a given ... In this paper we consider the

*fixed*-

*parameter*

*tractability*of a variety of different notions of

*distance*

*to*various different

*classes*C of

*sparse*

*graphs*. ...

##
###
Constant Thresholds Can Make Target Set Selection Tractable

2013
*
Theory of Computing Systems
*

corresponding

doi:10.1007/s00224-013-9499-3
fatcat:ykvmkfbzhje2dbfcyuhkzvunnm
*fixed*-*parameter**tractability*and (*parameterized*) hardness results. ... We contribute further insights into islands of*tractability*for Target Set Selection by spotting new*parameterizations*characterizing some*sparse**graphs*as well as some "cliquish"*graphs*and developing ... For the larger (thus "weaker" [19] )*parameter*"*distance**to*clique" (the minimum number of vertices*to*delete*to*make a*graph*a clique), however, TSS is*fixed*-*parameter**tractable*for both constant and ...##
###
Constant Thresholds Can Make Target Set Selection Tractable
[chapter]

2012
*
Lecture Notes in Computer Science
*

corresponding

doi:10.1007/978-3-642-34862-4_9
fatcat:xhx6vk3kjzgmlgcuhcmrgigrn4
*fixed*-*parameter**tractability*and (*parameterized*) hardness results. ... We contribute further insights into islands of*tractability*for Target Set Selection by spotting new*parameterizations*characterizing some*sparse**graphs*as well as some "cliquish"*graphs*and developing ... For the larger (thus "weaker" [19] )*parameter*"*distance**to*clique" (the minimum number of vertices*to*delete*to*make a*graph*a clique), however, TSS is*fixed*-*parameter**tractable*for both constant and ...##
###
Structure and Specification as Sources of Complexity

2009
*
Foundations of Software Technology and Theoretical Computer Science
*

Automata and Locality The following is a sampling of results on the

doi:10.4230/lipics.fsttcs.2009.2336
dblp:conf/fsttcs/Dawar09
fatcat:gubhh5istngmjcauyzu33d3cja
*fixed*-*parameter**tractability*of the first-order satisfaction problem on*classes*of*sparse**graphs*. ... It is easy*to*establish that problems such as INDEPENDENT SET are*fixed*-*parameter**tractable*on such*classes*. ...##
###
The Complexity of Satisfaction on Sparse Graphs
[chapter]

2010
*
Lecture Notes in Computer Science
*

It subsumes many natural

doi:10.1007/978-3-642-17493-3_1
fatcat:p2md6mgdnneollnsmsf23tondu
*parameterized**graph*problems (where,*fixing*the*parameter*, we can express the problem in first-order logic). • Vertex Cover; • Independent Set; • Dominating Set; • Network Centres ... That is, given a*graph*G and a formula ϕ of first-order logic in the language of*graphs*: What is the complexity of this,*parameterized*by the length of ϕ? ... First-order logic is*fixed*-*parameter**tractable*on M k . ...##
###
A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems
[article]

2022
*
arXiv
*
pre-print

The emphasis will be on positive results and the most common techniques for the design of

arXiv:2204.10526v1
fatcat:ua3pkqxtabatbbl6jydhy3i3b4
*fixed*-*parameter**tractable*algorithms. ... We survey both older and more recent work on the*parameterized*complexity of all three problems when*parameterized*by the number of tokens k. ... ., Independent Set, Dominating Set, and Connected Dominating Set*parameterized*by solution size k become*fixed*-*parameter**tractable*when restricted*to**sparse**graph**classes*, such as planar, bounded degree ...##
###
Spanners of bounded degree graphs

2011
*
Information Processing Letters
*

We prove that for

doi:10.1016/j.ipl.2010.10.021
fatcat:gw6jr2js4fchzbi62lscizrhj4
*fixed*k, w, the problem of deciding if a given*graph*has a k-spanner of treewidth w is*fixed*-*parameter**tractable*on*graphs*of bounded degree. ... In particular, this implies that finding a k-spanner that is a tree (a tree k-spanner) is*fixed*-*parameter**tractable*on*graphs*of bounded degree. ... They proved that the problem of finding a k-spanner of treewidth at most w in a given planar*graph*G is*fixed*-*parameter**tractable**parameterized*by k and w, and for every*fixed*k and w, this problem can ...##
###
Algorithmic Properties of Sparse Digraphs

2019
*
Symposium on Theoretical Aspects of Computer Science
*

The

doi:10.4230/lipics.stacs.2019.46
dblp:conf/stacs/KreutzerMMRS19
fatcat:k3zs6tfrpfbaxpkk4bfrnu5s7i
*classes*of directed*graphs*having those properties are very general*classes*of*sparse*directed*graphs*, as they include, on one hand, all*classes*of directed*graphs*whose underlying undirected*class*... has bounded expansion, such as planar, bounded-genus, and H-minor-free*graphs*, and on the other hand, they also contain*classes*whose underlying undirected*class*is not even nowhere dense. ... Once*fixed*-*parameter**tractability*is established, we turn our attention*to*the kernelisation problem for*Distance*-r Dominating Set. ...##
###
Progressive Algorithms for Domination and Independence

2019
*
Symposium on Theoretical Aspects of Computer Science
*

We demonstrate our approach by giving linear-time

doi:10.4230/lipics.stacs.2019.27
dblp:conf/stacs/FabianskiPST19
fatcat:wutum5aw6bho3clozgv7nl4hxy
*fixed*-*parameter*algorithms for the*Distance*-r Dominating Set problem (*parameterized*by the solution size) in a wide variety of restricted*graph**classes*... Similarly, for the*Distance*-r Independent Set problem the technique can be used*to*give a linear-time*fixed*-*parameter*algorithm on any nowhere dense*class*. ... Acknowledgements We thank Ehud Hrushovski for pointing us*to*the nfcp property. ...##
###
Recovering Sparse Graphs

2018
*
International Symposium on Mathematical Foundations of Computer Science
*

We derive as a corollary that if G is a

doi:10.4230/lipics.mfcs.2018.29
dblp:conf/mfcs/GajarskyK18
fatcat:bzr43lgahrewhbz6lb67dd67si
*graph**class*with bounded expansion, then the first order model checking is*fixed**parameter**tractable*in the*class*of all*graphs*that can obtained from a*graph*G ... We construct a*fixed**parameter*algorithm*parameterized*by d and k that takes as an input a*graph*G obtained from a d-degenerate*graph*G by complementing on at most k arbitrary subsets of the vertex set ... Both these problems are*fixed**parameter**tractable*when*parameterized*by d and k. ...##
###
Recovering sparse graphs
[article]

2018
*
arXiv
*
pre-print

We derive as a corollary that if G_0 is a

arXiv:1709.09985v3
fatcat:glc4eiz5l5ckjnafhycgxaxqma
*graph**class*with bounded expansion, then the first order model checking is*fixed**parameter**tractable*in the*class*of all*graphs*that can obtained from a*graph*... We construct a*fixed**parameter*algorithm*parameterized*by d and k that takes as an input a*graph*G' obtained from a d-degenerate*graph*G by complementing on at most k arbitrary subsets of the vertex set ... Both these problems are*fixed**parameter**tractable*when*parameterized*by d and k. ...##
###
On the Treewidth of Dynamic Graphs
[chapter]

2013
*
Lecture Notes in Computer Science
*

We show the application of these results

doi:10.1007/978-3-642-38768-5_32
fatcat:miynieup6rfdrkc46vf4w3zp7i
*to*problems in dynamic*graph*theory and dynamic extensions*to*static problems. ... In addition we demonstrate that certain widely used dynamic*graph**classes*have bounded local treewidth. ... Let C be any*class*of structures of bounded local treewidth. MC(C , FO) is*fixed*-*parameter**tractable*when*parameterized*by the length of the FO sentence. [16] .) ...##
###
On the treewidth of dynamic graphs

2014
*
Theoretical Computer Science
*

We show the application of these results

doi:10.1016/j.tcs.2013.12.024
fatcat:cbpjf6h62vdxxjdssqrw74h5vu
*to*problems in dynamic*graph*theory and dynamic extensions*to*static problems. ... In addition we demonstrate that certain widely used dynamic*graph**classes*have bounded local treewidth. ... Let C be any*class*of structures of bounded local treewidth. MC(C , FO) is*fixed*-*parameter**tractable*when*parameterized*by the length of the FO sentence. [16] .) ...##
###
Domination Above r-Independence: Does Sparseness Help?

2019
*
International Symposium on Mathematical Foundations of Computer Science
*

does the restriction

doi:10.4230/lipics.mfcs.2019.40
dblp:conf/mfcs/EinarsonR19
fatcat:2ufaxeeggvcgbmgjidmiqkkxk4
*to**sparse**graph**classes*help here? ... In the spirit of gap-*parameters*, we consider a parametrisation by the size of the "residual" set Our work aims*to*answer two questions: How does the constant r affect the*tractability*of the problem and ... For r = 3, the problem is W [2] -hard in general*graphs*but admits an XP-algorithm. In nowhere dense and bounded expansion*classes*, it is*fixed*-*parameter**tractable*. ...
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