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Some Parameterized Problems On Digraphs

2007
*
Computer journal
*

We survey results and open questions

doi:10.1093/comjnl/bxm039
fatcat:5yqonwpu2jgqfkuv7itpc7j3km
*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. ...##
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Acyclic coloring of special digraphs
[article]

2020
*
arXiv
*
pre-print

We introduce the first polynomial-time algorithm for the acyclic coloring

arXiv:2006.13911v3
fatcat:metx5oprwzefjnjf445a7ord2y
*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. ...##
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Parameterized complexity of the induced subgraph problem in directed graphs

2007
*
Information Processing Letters
*

In this Letter, we consider the

doi:10.1016/j.ipl.2007.05.005
fatcat:op6vygt5nzec5invx46fac5p3i
*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*. ...##
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Efficient computation of the oriented chromatic number of recursively defined digraphs
[article]

2021
*
arXiv
*
pre-print

In order to generalize the results

arXiv:2012.13764v2
fatcat:gh3myesexbdz3kwdi6gwdsco6y
*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*. ...##
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Parameterized Algorithms for Directed Maximum Leaf Problems
[article]

2007
*
arXiv
*
pre-print

We prove that finding a rooted subtree with at least k leaves in a

arXiv:cs/0702049v1
fatcat:6ly6553a25azhalba7h5zckhmi
*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). ...##
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On the Complexity of Broadcast Domination and Multipacking in Digraphs
[chapter]

2020
*
Lecture Notes in Computer Science
*

Finally, we give for both

doi:10.1007/978-3-030-48966-3_20
fatcat:543whpdysnflfp4xvacvvbwyre
*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. ...##
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Beyond bidimensionality: Parameterized subexponential algorithms on directed graphs

2013
*
Information and Computation
*

We develop two different methods to achieve subexponential time

doi:10.1016/j.ic.2013.11.006
fatcat:ohgatc74qzc43ndc75ga2esg5q
*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 ...##
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Parameterized algorithms for min-max multiway cut and list digraph homomorphism

2017
*
Journal of computer and system sciences (Print)
*

In this paper we design FPT-algorithms for two

doi:10.1016/j.jcss.2017.01.003
fatcat:2q2accwudrehlg4jt2wwxkb7sq
*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. ...##
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Beyond Bidimensionality: Parameterized Subexponential Algorithms on Directed Graphs
[article]

2010
*
arXiv
*
pre-print

We develop two different methods to achieve subexponential time

arXiv:1001.0821v1
fatcat:6ublf24drvfn3apo7vv7uynu4q
*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 ...##
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Directed branch-width: A directed analogue of tree-width
[article]

2020
*
arXiv
*
pre-print

Under

arXiv:2009.08903v1
fatcat:73hgbxj4ivdhbb5n42pvo7nwqu
*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. ...##
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Minimum leaf out-branching and related problems

2009
*
Theoretical Computer Science
*

We also consider transformations from two related

doi:10.1016/j.tcs.2009.03.036
fatcat:mtbbhza6izbctkkfhmlc7nxii4
*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*. ...##
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Parameterized Eulerian Strong Component Arc Deletion Problem on Tournaments
[article]

2011
*
arXiv
*
pre-print

In the

arXiv:1106.4454v2
fatcat:27pnytiyk5auzh6mk5hx5ydfwm
*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. ...##
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Resolving Infeasibility of Linear Systems: A Parameterized Approach

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. ...

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

2018
*
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
*

We also show that λ-VCS is FPT

doi:10.1137/1.9781611975031.180
dblp:conf/soda/Bang-JensenBKMR18
fatcat:hthxf5myyjbwjemewjba3rd4k4
*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. ...##
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Minimum Leaf Out-branching and Related Problems
[article]

2008
*
arXiv
*
pre-print

We also consider transformations from two related

arXiv:0801.1979v3
fatcat:owzbuxpjefakxe5lrjbql4u6iy
*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*. ...
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