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Some Parameterized Problems On Digraphs

G. Gutin, A. Yeo
2007 Computer journal  
We survey results and open questions on complexity of parameterized problems on digraphs.  ...  The problems include the feedback vertex and arc set problems, induced subdigraph problems and directed k-leaf problems. We also prove some new results on the topic.  ...  Other parameterized problems on digraphs In this section we give a short overview of some other papers on the topic.  ... 
doi:10.1093/comjnl/bxm039 fatcat:5yqonwpu2jgqfkuv7itpc7j3km

Acyclic coloring of special digraphs [article]

Frank Gurski and Dominique Komander and Carolin Rehs
2020 arXiv   pre-print
We introduce the first polynomial-time algorithm for the acyclic coloring problem on digraphs of constant directed clique-width.  ...  This allows us to carry over the W[1]-hardness and lower bounds for running times of the chromatic number problem parameterized by clique-width to the dichromatic number problem parameterized by directed  ...  Corollary 4. 6 6 The Dichromatic Number problem is W[1]-hard on symmetric digraphs and thus, on all digraphs when parameterized by directed clique-width. Figure 1 : 1 Digraph in Example 4.7.  ... 
arXiv:2006.13911v3 fatcat:metx5oprwzefjnjf445a7ord2y

Parameterized complexity of the induced subgraph problem in directed graphs

Venkatesh Raman, Somnath Sikdar
2007 Information Processing Letters  
In this Letter, we consider the parameterized complexity of the following problem: Given a hereditary property P on digraphs, an input digraph D and a positive integer k, does D have an induced subdigraph  ...  These results are among the very few parameterized complexity results on directed graphs.  ...  with c colors, for some constant c 1, (5) planar, (6) a line digraph.  ... 
doi:10.1016/j.ipl.2007.05.005 fatcat:op6vygt5nzec5invx46fac5p3i

Efficient computation of the oriented chromatic number of recursively defined digraphs [article]

Frank Gurski and Dominique Komander and Marvin Lindemann
2021 arXiv   pre-print
In order to generalize the results on computing the oriented chromatic number of special graph classes, we consider the parameterized complexity of the Oriented Chromatic Number problem by so-called structural  ...  In this paper we consider the Oriented Chromatic Number problem on classes of recursively defined oriented graphs.  ...  Parameterized Results A parameterized problem is a pair (Π, κ) , where Π is a decision problem, I the set of all instances of Π and κ : I → N a so-called parameterization.  ... 
arXiv:2012.13764v2 fatcat:gh3myesexbdz3kwdi6gwdsco6y

Parameterized Algorithms for Directed Maximum Leaf Problems [article]

Noga Alon, Fedor Fomin, Gregory Gutin, Michael Krivelevich, Saket Saurabh
2007 arXiv   pre-print
We prove that finding a rooted subtree with at least k leaves in a digraph is a fixed parameter tractable problem.  ...  This settles completely an open question of Fellows and solves another one for digraphs in L.  ...  The parameterized complexity of the k-DMLOB problem for all digraphs remains open. For some subfamilies of L, one can obtain better bounds on ℓ s (D).  ... 
arXiv:cs/0702049v1 fatcat:6ly6553a25azhalba7h5zckhmi

On the Complexity of Broadcast Domination and Multipacking in Digraphs [chapter]

Florent Foucaud, Benjamin Gras, Anthony Perez, Florian Sikora
2020 Lecture Notes in Computer Science  
Finally, we give for both problems polynomial-time algorithms for some subclasses of acyclic digraphs.  ...  Moreover, when parameterized by the solution cost/solution size, we show that the problems are respectively W[2]-hard and W[1]-hard.  ...  Parameterized Complexity. A parameterized problem is a decision problem together with a parameter, that is, an integer k depending on the instance.  ... 
doi:10.1007/978-3-030-48966-3_20 fatcat:543whpdysnflfp4xvacvvbwyre

Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs

Frederic Dorn, Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh
2013 Information and Computation  
We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems.  ...  We obtain an algorithm solving the problem in time 2 O( √ k log k) + n O(1) on directed graphs whose underlying undirected graph excludes some fixed apex graph H as a minor.  ...  We develop two different methods to achieve subexponential time parameterized algorithms for digraph problems when the input graph can be embedded on some surface or the underlying undirected graph excludes  ... 
doi:10.1016/j.ic.2013.11.006 fatcat:ohgatc74qzc43ndc75ga2esg5q

Parameterized algorithms for min-max multiway cut and list digraph homomorphism

Eun Jung Kim, Christophe Paul, Ignasi Sau, Dimitrios M. Thilikos
2017 Journal of computer and system sciences (Print)  
In this paper we design FPT-algorithms for two parameterized problems.  ...  Our approach introduces a general problem, called List Allocation, whose expressive power permits the design of parameterized reductions of both aforementioned problems to it.  ...  We would like to thank the anonymous referees of an earlier version of this paper for their thorough remarks and suggestions that improved the presentation and some proofs of the paper.  ... 
doi:10.1016/j.jcss.2017.01.003 fatcat:2q2accwudrehlg4jt2wwxkb7sq

Beyond Bidimensionality: Parameterized Subexponential Algorithms on Directed Graphs [article]

Frederic Dorn, Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman and Saket Saurabh
2010 arXiv   pre-print
We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems.  ...  We obtain an algorithm solving the problem in time 2^O(√(k) k) + n^O(1) on directed graphs whose underlying undirected graph excludes some fixed apex graph H as a minor.  ...  We develop two different methods to achieve subexponential time parameterized algorithms for digraph problems when the input graph can be embedded on some surface or the underlying undirected graph excludes  ... 
arXiv:1001.0821v1 fatcat:6ublf24drvfn3apo7vv7uynu4q

Directed branch-width: A directed analogue of tree-width [article]

Benjamin Merlin Bumpus, Kitty Meeks, William Pettersson
2020 arXiv   pre-print
Under parameterizations by directed branch-width we obtain linear time algorithms for many problems, such as directed Hamilton path and Max-Cut, which are hard when parameterized by other known directed  ...  More generally, we obtain an algorithmic meta-theorem for the model-checking problem for a restricted variant of MSO_2-logic on classes of bounded directed branch-width.  ...  Let Π be a decision problem on digraphs which is in FPT parameterized by underlying tree-width.  ... 
arXiv:2009.08903v1 fatcat:73hgbxj4ivdhbb5n42pvo7nwqu

Minimum leaf out-branching and related problems

Gregory Gutin, Igor Razgon, Eun Jung Kim
2009 Theoretical Computer Science  
We also consider transformations from two related problems, the minimum path covering and the maximum internal out-tree problems into MinLOB, which imply that some parameterizations of the two problems  ...  We prove that MinLOB is polynomial-time solvable for acyclic digraphs. In general, MinLOB is NPhard and we consider three parameterizations of MinLOB.  ...  Let Π be a parameterized problem.  ... 
doi:10.1016/j.tcs.2009.03.036 fatcat:mtbbhza6izbctkkfhmlc7nxii4

Parameterized Eulerian Strong Component Arc Deletion Problem on Tournaments [article]

Robert Crowston, Gregory Gutin, Mark Jones, Anders Yeo
2011 arXiv   pre-print
In the problem Min-DESC, we are given a digraph D and an integer k, and asked if there exists a set A' of at most k arcs in D, such that if we remove the arcs of A', in the resulting digraph every strong  ...  Min-DESC is NP-hard; Cechlárová and Schlotter (IPEC 2010) asked if the problem is fixed-parameter tractable when parameterized by k. We consider the subproblem of Min-DESC when D is a tournament.  ...  Introduction A digraph D is strongly connected if for every x, y ∈ V (D) there is a directed path in D from x to y. In particular, the digraph consisting of just one vertex is strongly connected.  ... 
arXiv:1106.4454v2 fatcat:27pnytiyk5auzh6mk5hx5ydfwm

Resolving Infeasibility of Linear Systems: A Parameterized Approach

Alexander Göke, Lydia Mirabel Mendoza Cadena, Matthias Mnich, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
On the one hand, we establish parameterized intractability (W[1]-hardness) results even in very restricted settings.  ...  Our algorithms capture the case of Directed Feedback Arc Set, a fundamental parameterized problem whose fixed-parameter tractability was shown by Chen et al.  ...  Acknowledgements We thank an anonymous reviewer of an earlier version for a suggestion on run time improvements.  ... 
doi:10.4230/lipics.ipec.2019.17 dblp:conf/iwpec/GokeCM19 fatcat:sgby4wvmi5ep7duyx3d5noigo4

Parameterized Algorithms for Survivable Network Design with Uniform Demands [chapter]

Jørgen Bang-Jensen, Manu Basavaraju, Kristine Vitting Klinkby, Pranabendu Misra, M. S. Ramanujan, Saket Saurabh, Meirav Zehavi
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We also show that λ-VCS is FPT on digraphs; however the problem on undirected graphs remains open.  ...  We show that λ-ECS is fixed-parameter tractable (FPT) for both graphs and digraphs even if the (di)graph has nonnegative real weights on the edges and the objective is to exclude from H, some edges of  ...  It is important to point out another parameterization of p-λ-ECS on digraphs when λ = 1.  ... 
doi:10.1137/1.9781611975031.180 dblp:conf/soda/Bang-JensenBKMR18 fatcat:hthxf5myyjbwjemewjba3rd4k4

Minimum Leaf Out-branching and Related Problems [article]

G. Gutin, I. Razgon, E.J. Kim
2008 arXiv   pre-print
We also consider transformations from two related problems, the minimum path covering and the maximum internal out-tree problems into MinLOB, which imply that some parameterizations of the two problems  ...  We prove that MinLOB is polynomial-time solvable for acyclic digraphs. In general, MinLOB is NP-hard and we consider three parameterizations of MinLOB.  ...  Let Π be a parameterized problem.  ... 
arXiv:0801.1979v3 fatcat:owzbuxpjefakxe5lrjbql4u6iy
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