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A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs
[article]

2018
*
arXiv
*
pre-print

To this end, we develop

arXiv:1604.06302v3
fatcat:ezo26nmmn5dbdm3dbb3qtzp4y4
*a*general two-stage*framework*which consists of efficiently solving*a**problem*-specific number*problem*and transferring its solution to*a*solution*for*the*graph**problem*by applying ... There has been intensive work on the*parameterized*complexity of the typically NP-hard task to edit undirected*graphs*into*graphs*fulfilling certain given vertex*degree*constraints. ... The*Framework*Our goal is to develop*a**framework**for*deriving fixed-parameter tractability*for**a*general class of*completion**problems**in**directed**graphs*. ...##
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A Parameterized Algorithmics Framework for Degree Sequence Completion Problems in Directed Graphs

2018
*
Algorithmica
*

as used

doi:10.1007/s00453-018-0494-6
fatcat:24mcugsrujflblsvg5adonymbq
*in*the undirected case seem not to work*for*the*directed*case. constructing*a*specific network topology) or "*graph*realization"*problems*. ... To this end, our general two-stage*framework*consists of efficiently solving*a**problem*-specific number*problem*transferring its solution to*a*solution*for*the*graph**problem*by applying flow computations ... |, 10:6*A**Framework**for**Degree**Sequence**Completion**Problems**in**Directed**Graphs*As*a*first step, we prove that these sets defined above can be computed efficiently. ...##
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Introduction to Reconfiguration

2018
*
Algorithms
*

Work

doi:10.3390/a11040052
fatcat:nmokeftdqrgtpdyh2ohl3tchce
*in*the area encompasses both structural questions (Is the reconfiguration*graph*connected?) and*algorithmic*ones (How can one find the shortest*sequence*of steps between two solutions?) ... Reconfiguration is concerned with relationships among solutions to*a**problem*instance, where the reconfiguration of one solution to another is*a**sequence*of steps such that each step produces an intermediate ... To the contrary, although VERTEX COVER is NP-*complete*when restricted to planar*graphs*, reachability is*in*FPT*parameterized*by*for*planar*graphs*[49] and*graphs*of*degree*at most d, d ≥ 4 [54] . ...##
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Everything you always wanted to know about the parameterized complexity of Subgraph Isomorphism (but were afraid to ask)

2014
*
Symposium on Theoretical Aspects of Computer Science
*

Given two

doi:10.4230/lipics.stacs.2014.542
dblp:conf/stacs/MarxP14
fatcat:dy4trfjwkvhj3i2tzcvrguedyi
*graphs*H and G, the Subgraph Isomorphism*problem*asks if H is isomorphic to*a*subgraph of G. While NP-hard*in*general,*algorithms*exist*for*various*parameterized*versions of the*problem*. ... We develop*a**framework*involving 10 relevant parameters*for*each of H and G (such as treewidth, pathwidth, genus, maximum*degree*, number of vertices, number of components, etc.), and ask if an*algorithm*... Conclusions*In*this paper we have developed*a**framework**for*studying different*parameterizations*of Subgraph Isomorphism and*completely*answered every question arising*in*this*framework*. ...##
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A survey of parameterized algorithms and the complexity of edge modification
[article]

2020
*
arXiv
*
pre-print

The survey provides an overview of the developing area of

arXiv:2001.06867v2
fatcat:6ogysat6n5drpbxsvs63zjmega
*parameterized**algorithms**for**graph*modification*problems*. ... We concentrate on edge modification*problems*, where the task is to change*a*small number of adjacencies*in**a**graph**in*order to satisfy some required property. ... We thank Marcin Pilipczuk, William Lochet, and Dekel Tsur*for*helpful comments. References ...##
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On problems without polynomial kernels

2009
*
Journal of computer and system sciences (Print)
*

Our evidence relies on hypothesis made

doi:10.1016/j.jcss.2009.04.001
fatcat:fko3t354mrayflrl2lxuzg6ez4
*in*the classical world (i.e. non-parametric complexity), and revolves around*a*new type of*algorithm**for*classical decision*problems*, called*a*distillation*algorithm*...*In*this paper we develop*a**framework*which allows showing that*a*wide range of FPT*problems*do not have polynomial kernels. ... The fourth author would also like to especially thank Moritz Müller*for*reviewing several preliminary versions, and*for*the countless (and sometimes endless) debates on related topics. ...##
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Incremental Optimization of Independent Sets under Reachability Constraints
[article]

2018
*
arXiv
*
pre-print

On the other hand, we give

arXiv:1804.09422v1
fatcat:rjjvttvz6jdhxcsbt3h2qjynze
*a*fixed-parameter*algorithm*when*parameterized*by s+d; this result implies that the*problem**parameterized*only by s is fixed-parameter tractable*for*planar*graphs*, and*for*bounded ... On the other hand, we give*a*linear-time*algorithm*to solve the*problem**for*chordal*graphs*. ... Acknowledgments We thank Tatsuhiko Hatanaka*for*his insightful suggestions on this new*framework*. ...##
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Clique Cover and Graph Separation: New Incompressibility Results
[chapter]

2012
*
Lecture Notes in Computer Science
*

Please see the 'permanent WRAP url' above

doi:10.1007/978-3-642-31594-7_22
fatcat:rnkjsck5eff2dbn34p5hpcpgla
*for*details on accessing the published version and note that access may require*a*subscription. ... We would like to thank Jakub Onufry Wojtaszczyk*for*some early discussions on the kernelization of the*graph*separation*problems*. ...*for*most*graph*separation*problems**in**directed**graphs*. ...##
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Clique Cover and Graph Separation

2014
*
ACM Transactions on Computation Theory
*

Please see the 'permanent WRAP url' above

doi:10.1145/2594439
fatcat:ad7g3ncsz5h3bie6vi5lvrq6ta
*for*details on accessing the published version and note that access may require*a*subscription. ... We would like to thank Jakub Onufry Wojtaszczyk*for*some early discussions on the kernelization of the*graph*separation*problems*. ...*for*most*graph*separation*problems**in**directed**graphs*. ...##
###
A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems
[article]

2022
*
arXiv
*
pre-print

Many

arXiv:2204.10526v1
fatcat:ua3pkqxtabatbbl6jydhy3i3b4
*algorithmic*questions present themselves*in*the form of reconfiguration*problems*: Given the description of an initial system state and the description of*a*target state, is it possible to transform ...*A**graph*vertex-subset*problem*defines which subsets of the vertices of an input*graph*are feasible solutions. We view*a*feasible solution as*a*set of tokens placed on the vertices of the*graph*. ... From an*algorithmic*standpoint, the authors*in*[34] showed that DSR-TJ is PSPACE-*complete*on split*graphs*, bipartite*graphs*,*graphs*of bounded bandwidth and planar*graphs*of maximum*degree*six. ...##
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Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

2019
*
European Symposium on Algorithms
*

We develop

doi:10.4230/lipics.esa.2019.37
dblp:conf/esa/DemaineGKLLSVP19
fatcat:sa6gr2pm3rggpdb5pehdxtmk6e
*a**framework**for*generalizing approximation*algorithms*from the structural*graph**algorithm*literature so that they apply to*graphs*somewhat close to that class (*a*scenario we expect is common ... To enable this*framework*, we develop new editing*algorithms*that find the approximatelyfewest edits required to bring*a*given*graph*into one of*a*few important*graph*classes (*in*some cases these are bicriteria ... Acknowledgements We thank Abida Haque and Adam Hesterberg*for*helpful initial discussions, Nicole Wein*for*providing helpful references on bounded degeneracy*problems*, and Michael O'Brien*for*helpful comments ...##
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Parameterized Complexity of Graph Constraint Logic

2015
*
International Symposium on Parameterized and Exact Computation
*

*Graph*constraint logic is

*a*

*framework*introduced by Hearn and Demaine, which provides several

*problems*that are often

*a*convenient starting point

*for*reductions. ... maximum

*degree*of the underlying constraint

*graph*as parameters. ...

*in*NP, however, it is not clear whether there exists

*a*pseudopolynomial

*algorithm*

*for*the

*problem*, so we can not claim weak NP-

*completeness*. ...

##
###
Parameterized Complexity of Graph Constraint Logic
[article]

2015
*
arXiv
*
pre-print

*Graph*constraint logic is

*a*

*framework*introduced by Hearn and Demaine, which provides several

*problems*that are often

*a*convenient starting point

*for*reductions. ... As

*a*main result we show that restricted NCL remains PSPACE-

*complete*on

*graphs*of bounded bandwidth, strengthening Hearn and Demaine's

*framework*. ... It is an open

*problem*whether there exists

*a*pseudopolynomial

*algorithm*

*for*this case, or if the

*problem*is also strongly NP-

*complete*. ...

##
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The Computer Journal Special Issue on Parameterized Complexity: Foreword by the Guest Editors

2007
*
Computer journal
*

Similarly, Vertex Cover can be kernelized

doi:10.1093/comjnl/bxm111
fatcat:jhqptpkwj5c63a6t6xuqgj3dju
*in*polynomial time to*a**graph*of minimum*degree*4 (*in*fact, "almost" minimum*degree*5). ...*For*example, Grohe and Grüber [GG07] have recently shown that while determining if*a**directed**graph*has at least k vertex-disjoint*directed*cycles is hard*for*W [1], one can*in*FPT time either determine ...##
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Blow-Ups, Win/Win's, and Crown Rules: Some New Directions in FPT
[chapter]

2003
*
Lecture Notes in Computer Science
*

This survey reviews the basic notions of

doi:10.1007/978-3-540-39890-5_1
fatcat:jojjzpn4fffedjarzcwieynllm
*parameterized*complexity, and describes some new approaches to designing FPT*algorithms*and*problem*reductions*for**graph**problems*. ... The*parameterized*complexity*framework*is*a*two-dimensional*framework**for*complexity analysis, where the first dimension is the overall imput size n. ... Dominating Set is W [2]-*complete*, while its parametric dual is*in*FPT. There are O * (2 O(k) ) FPT*algorithms**for*many*parameterized**problems*, such as Vertex Cover. ...
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