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Some Parameterized Problems On Digraphs
2007
Computer journal
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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]
2020
arXiv
pre-print
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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
2007
Information Processing Letters
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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]
2021
arXiv
pre-print
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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]
2007
arXiv
pre-print
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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]
2020
Lecture Notes in Computer Science
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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
2013
Information and Computation
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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
2017
Journal of computer and system sciences (Print)
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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]
2010
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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
2009
Theoretical Computer Science
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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]
2011
arXiv
pre-print
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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
2019
International Symposium on Parameterized and Exact Computation
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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]
2018
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
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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]
2008
arXiv
pre-print
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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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