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A Cubic Kernel for Feedback Vertex Set and Loop Cutset
2009
Theory of Computing Systems
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This kernelization algorithm can be used as the first step of an FPT algorithm for FEEDBACK VERTEX SET, but also as a preprocessing heuristic for FEEDBACK VERTEX SET. ...
feedback vertex set of G. ...
Acknowledgements We thank the anonymous referees of the paper for useful comments. ...
doi:10.1007/s00224-009-9234-2
fatcat:cwq2aws44bhmhd4r3qxbdqcvoq
A Cubic Kernel for Feedback Vertex Set
[chapter]
STACS 2007
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This kernelization algorithm can be used as the first step of an FPT algorithm for Feedback Vertex Set, but also as a preprocessing heuristic for Feedback Vertex Set. ...
Moreover, if G has a feedback vertex set of size at most k , then a minimum size feedback vertex set of G directly gives a minimum size feedback vertex set of size k . ...
We claim that for each set S ⊆ V , S is a feedback vertex set in G, if and only if S is a feedback vertex set in G . ...
doi:10.1007/978-3-540-70918-3_28
dblp:conf/stacs/Bodlaender07
fatcat:blfcrzsppnfnrdn5fb2zo2cbbm
Vertex Cover Kernelization Revisited: Upper and Lower Bounds for a Refined Parameter
2011
Symposium on Theoretical Aspects of Computer Science
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be reduced to a polynomial in the size of the minimum FVS In the language of parameterized complexity: Vertex Cover parameterized by the size of a feedback vertex set admits a cubic-The Weighted Vertex ...
Vertex Cover using a "refined" parameter: Feedback Vertex Number We have studied data reduction for Vertex Cover using a "refined" parameter: Feedback Vertex Number Kernel with O(|X| 3 ) vertices Usage ...
degree of the polynomial: cubic to quadratic? ...
doi:10.4230/lipics.stacs.2011.177
dblp:conf/stacs/JansenB11
fatcat:v6mfndllc5bsxctpwhranx52wa
A quadratic kernel for feedback vertex set
[chapter]
2009
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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set of size at most k iff G has a feedback vertex set of size at most k . ...
This result improves a previous O(k 11 ) kernel of Burrage et al. [6] , and a more recent cubic kernel of Bodlaender [3]. This problem was communicated by Fellows in [5] . ...
We provide in this paper a quadratic kernel for FEEDBACK VERTEX SET which reduces the input graph G to a graph G with size at most 5k 2 +k. ...
doi:10.1137/1.9781611973068.13
fatcat:pnzy5eafojdsjcmu3swyzg4fym
A 4k2kernel for feedback vertex set
2010
ACM Transactions on Algorithms
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set of size at most k iff G has a feedback vertex set of size at most k . ...
This result improves a previous O(k 11 ) kernel of Burrage et al. [5] , and a more recent cubic kernel of Bodlaender [3] . This problem was communicated by Fellows in [4] . ...
We provide in this paper a quadratic kernel for FEEDBACK VERTEX SET which reduces the input graph G to a graph G with size at most 4k 2 . ...
doi:10.1145/1721837.1721848
fatcat:raq6svwq6ncehczv6onenivzly
Safe Approximation and Its Relation to Kernelization
[chapter]
2012
Lecture Notes in Computer Science
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We introduce a notion of approximation, called safe approximation, for minimization problems that are subset problems. ...
We demonstrate how the notion of safe approximation can be useful in designing kernelization algorithms for certain fixed-parameter tractable problems. ...
The authors would like to thank Bart Jansen for suggesting the nice example used in the proof of Theorem 4. ...
doi:10.1007/978-3-642-28050-4_14
fatcat:2c7xqcqavrh7jae74ms2ndbowe
On Parameterized Independent Feedback Vertex Set
[chapter]
2011
Lecture Notes in Computer Science
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We investigate a generalization of the classical Feedback Vertex Set (FVS) problem from the point of view of parameterized algorithms. ...
We show that IFVS can be solved in time O(5 k n O(1) ) time where n is the number of vertices in the input graph G, and obtain a cubic (O(k 3 )) kernel for the problem. ...
A Cubic Kernel In this section we describe a kernelization algorithm which yields a kernel of size O(k 3 ) for the IFVS problem. ...
doi:10.1007/978-3-642-22685-4_9
fatcat:enmtafu2unf6hb2kgesdvr2pum
Page 5811 of Mathematical Reviews Vol. , Issue 96j
[page]
1996
Mathematical Reviews
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new bound on the feedback vertex sets in cubic graphs. ...
Summary: “For a graph G, a subset of vertices D is a k-dominating set of G if for each vertex x not in D, x is at distance at most k from some vertex in D. ...
An Improved FPT Algorithm and Quadratic Kernel for Pathwidth One Vertex Deletion
[chapter]
2010
Lecture Notes in Computer Science
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In this paper we improve these results by showing a quadratic kernel and a 4.65 k n O(1) algorithm. ...
Recently Philip et al. [14] initiated the study of the parameterized complexity of POVD and have shown a quartic kernel and a 7 k n O(1) algorithm. ...
One of the most extensively studied problems in the parameterized complexity community, FEEDBACK VERTEX SET, asks for a set of vertices of size at most k such that their deletion results in a graph of ...
doi:10.1007/978-3-642-17493-3_11
fatcat:orqu3ziug5ez7geggcmlmvfhua
Parameterized Aspects of Triangle Enumeration
[article]
2018
arXiv
pre-print
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tuned for large graphs). ...
Motivated by the fact that the worst-case running time is cubic, we perform a systematic parameterized complexity study of triangle enumeration. ...
We thank Mark Ortmann for fruitful discussions on obstacles for practical algorithms. ...
arXiv:1702.06548v4
fatcat:b7z7jh6tjngxfazvfppoqkiu4y
Vertex Cover Kernelization Revisited
2012
Theory of Computing Systems
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We give a kernel for Vertex Cover with a number of vertices that is cubic in fvs(G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into ...
In this paper we consider the Vertex Cover problem with a different parameter, the size fvs(G) of a minimum feedback vertex set for G. ...
Acknowledgements We are grateful to the anonymous referees, whose suggestions significantly improved the exposition of our results and decreased the running time of the kernelization procedure. ...
doi:10.1007/s00224-012-9393-4
fatcat:qfkejrlmfrfq5kwihwau2ieqwi
On the Parameterized Complexity of Reconfiguration Problems
2016
Algorithmica
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Hitting Set and Feedback Vertex Set, all parameterized by k. ...
For most of the results in this paper, S and T are subsets of vertices of a given graph and a reconfiguration step adds or deletes a vertex. ...
The second author wishes to thank Marcin Kamiński for suggesting the examination of reconfiguration in the parameterized setting. ...
doi:10.1007/s00453-016-0159-2
fatcat:qretakdj4nhhtgipvk4fyjlhsq
On the Parameterized Complexity of Reconfiguration Problems
[chapter]
2013
Lecture Notes in Computer Science
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Hitting Set and Feedback Vertex Set, all parameterized by k. ...
For most of the results in this paper, S and T are subsets of vertices of a given graph and a reconfiguration step adds or deletes a vertex. ...
The second author wishes to thank Marcin Kamiński for suggesting the examination of reconfiguration in the parameterized setting. ...
doi:10.1007/978-3-319-03898-8_24
fatcat:fg5zfk6ov5egtda4i2hqvhbocu
On Parameterized Independent Feedback Vertex Set
2012
Theoretical Computer Science
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We investigate a generalization of the classical Feedback Vertex Set (FVS) problem from the point of view of parameterized algorithms. ...
We show that IFVS can be solved in O(5 k n O(1) ) time, where n is the number of vertices in the input graph G, and obtain a cubic (O(k 3 )) kernel for the problem. ...
A cubic kernel In this section, we describe a kernelization algorithm which yields a kernel of size O(k 3 ) for the IFVS problem. ...
doi:10.1016/j.tcs.2012.02.012
fatcat:rgtgkd2snnbf5mb3q2rymiraky
Parameterized Aspects of Triangle Enumeration
[chapter]
2017
Lecture Notes in Computer Science
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In particular, we provide enumerative problem kernels with respect to the parameters "feedback edge number" and "vertex deletion distance to d-degeneracy". ...
Partially based on the corresponding data reduction algorithms, we provide "faster" algorithms for parameters such as feedback edge number, vertex deletion distance to d-degeneracy (also with additional ...
feedback vertex set (distance to 1-degenerate graphs). ...
doi:10.1007/978-3-662-55751-8_9
fatcat:yuuptmzjvjearabsr7kzg6vdui
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