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

Robert Bredereck, Vincent Froese, Marcel Koseler, Marcelo Garlet Millani, André Nichterlein, Rolf Niedermeier
2018 arXiv   pre-print
To this end, we develop 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.  ... 
arXiv:1604.06302v3 fatcat:ezo26nmmn5dbdm3dbb3qtzp4y4

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

Robert Bredereck, Vincent Froese, Marcel Koseler, Marcelo Garlet Millani, André Nichterlein, Rolf Niedermeier
2018 Algorithmica  
as used 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.  ... 
doi:10.1007/s00453-018-0494-6 fatcat:24mcugsrujflblsvg5adonymbq

Introduction to Reconfiguration

Naomi Nishimura
2018 Algorithms  
Work 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] .  ... 
doi:10.3390/a11040052 fatcat:nmokeftdqrgtpdyh2ohl3tchce

Everything you always wanted to know about the parameterized complexity of Subgraph Isomorphism (but were afraid to ask)

Dániel Marx, Michal Pilipczuk, Marc Herbstritt
2014 Symposium on Theoretical Aspects of Computer Science  
Given two 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.  ... 
doi:10.4230/lipics.stacs.2014.542 dblp:conf/stacs/MarxP14 fatcat:dy4trfjwkvhj3i2tzcvrguedyi

A survey of parameterized algorithms and the complexity of edge modification [article]

Christophe Crespelle, Pål Grønås Drange, Fedor V. Fomin, Petr A. Golovach
2020 arXiv   pre-print
The survey provides an overview of the developing area of 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  ... 
arXiv:2001.06867v2 fatcat:6ogysat6n5drpbxsvs63zjmega

On problems without polynomial kernels

Hans L. Bodlaender, Rodney G. Downey, Michael R. Fellows, Danny Hermelin
2009 Journal of computer and system sciences (Print)  
Our evidence relies on hypothesis made 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.  ... 
doi:10.1016/j.jcss.2009.04.001 fatcat:fko3t354mrayflrl2lxuzg6ez4

Incremental Optimization of Independent Sets under Reachability Constraints [article]

Takehiro Ito, Haruka Mizuta, Naomi Nishimura, Akira Suzuki
2018 arXiv   pre-print
On the other hand, we give 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.  ... 
arXiv:1804.09422v1 fatcat:rjjvttvz6jdhxcsbt3h2qjynze

Clique Cover and Graph Separation: New Incompressibility Results [chapter]

Marek Cygan, Stefan Kratsch, Marcin Pilipczuk, Michał Pilipczuk, Magnus Wahlström
2012 Lecture Notes in Computer Science  
Please see the 'permanent WRAP url' above 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.  ... 
doi:10.1007/978-3-642-31594-7_22 fatcat:rnkjsck5eff2dbn34p5hpcpgla

Clique Cover and Graph Separation

Marek Cygan, Stefan Kratsch, Marcin Pilipczuk, Michał Pilipczuk, Magnus Wahlström
2014 ACM Transactions on Computation Theory  
Please see the 'permanent WRAP url' above 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.  ... 
doi:10.1145/2594439 fatcat:ad7g3ncsz5h3bie6vi5lvrq6ta

A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems [article]

Nicolas Bousquet and Amer E. Mouawad and Naomi Nishimura and Sebastian Siebertz
2022 arXiv   pre-print
Many 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.  ... 
arXiv:2204.10526v1 fatcat:ua3pkqxtabatbbl6jydhy3i3b4

Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, Andrew Van Der Poel, Michael Wagner
2019 European Symposium on Algorithms  
We develop 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  ... 
doi:10.4230/lipics.esa.2019.37 dblp:conf/esa/DemaineGKLLSVP19 fatcat:sa6gr2pm3rggpdb5pehdxtmk6e

Parameterized Complexity of Graph Constraint Logic

Tom C. Van Der Zanden, Marc Herbstritt
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.  ... 
doi:10.4230/lipics.ipec.2015.282 dblp:conf/iwpec/Zanden15 fatcat:b6zwiy3j6ra7bkv42dnpye5sp4

Parameterized Complexity of Graph Constraint Logic [article]

Tom C. van der Zanden
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.  ... 
arXiv:1509.02683v1 fatcat:wgyz52d3rbcbhmm3n6f6ve3dmq

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

R. G. Downey, M. R. Fellows, M. A. Langston
2007 Computer journal  
Similarly, Vertex Cover can be kernelized 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  ... 
doi:10.1093/comjnl/bxm111 fatcat:jhqptpkwj5c63a6t6xuqgj3dju

Blow-Ups, Win/Win's, and Crown Rules: Some New Directions in FPT [chapter]

Michael R. Fellows
2003 Lecture Notes in Computer Science  
This survey reviews the basic notions of 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.  ... 
doi:10.1007/978-3-540-39890-5_1 fatcat:jojjzpn4fffedjarzcwieynllm
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