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Linear-time Kernelization for Feedback Vertex Set
[article]

2017
*
arXiv
*
pre-print

This is the first

arXiv:1608.01463v3
fatcat:qg7pomkxnzbyve4tsexgyq53uy
*linear*-*time*polynomial-size*kernel**for**Feedback**Vertex**Set*. ... We note that under the assumption of NP⊆coNP/poly,*Feedback**Vertex**Set*does not admit an O(k^2-ϵ)-size*kernel**for*any ϵ>0. ... Our Contribution In this paper, we propose a*linear*-*time*quadratic-size*kernel**for**Feedback**Vertex**Set*. This is the first*linear*-*time*polynomial-size*kernel**for*this problem. ...##
###
Vertex Cover Kernelization Revisited: Upper and Lower Bounds for a Refined Parameter

2011
*
Symposium on Theoretical Aspects of Computer Science
*

*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 ... Cover using a "refined" parameter:

*Feedback*

*Vertex*Number

*Kernel*with O(|X| 3 ) vertices Usage of

*vertex*weights affects kernelizability No polynomial

*kernel*

*for*weighted problem parameterized by ...

##
###
The Power of Linear-Time Data Reduction for Maximum Matching

2020
*
Algorithmica
*

As a warm-up we first show that a subset of our data reduction rules

doi:10.1007/s00453-020-00736-0
fatcat:jcfxcsmjsrhftb6ieutarcmjeq
*for*the "*feedback**vertex**set**kernel*" also yields a*linear*-*time*computable*linear*-size*kernel**for*the typically much larger parameter ... Notably, there is a trivial*linear*-*time*algorithm*for*computing the*feedback*edge number and there is a*linear*-*time*factor-4 approximation algorithm*for*the*feedback**vertex*number [1] . ... Warm-Up: Parameter*Feedback*Edge Number We provide a*linear*-*time*computable*linear*-size*kernel**for*Matching parameterized by the*feedback*edge number, that is, the size of a minimum*feedback*edge*set*. ...##
###
The Undirected Feedback Vertex Set Problem Has a Poly(k) Kernel
[chapter]

2006
*
Lecture Notes in Computer Science
*

Resolving a noted open problem, we show that the Undirected

doi:10.1007/11847250_18
fatcat:gjnuswvyvbb2jlsnrxptg2cdga
*Feedback**Vertex**Set*problem, parameterized by the size of the solution*set*of vertices, is in the parameterized complexity class P oly(k), that ... Our main result shows an O(k 11 )*kernelization*bound. ... It makes sense to ask if the Undirected*Feedback**Vertex**Set*problem might admit a*linear*-size Turing*kernelization*. ...##
###
Kernels for Feedback Arc Set In Tournaments
[article]

2009
*
arXiv
*
pre-print

The

arXiv:0907.2165v2
fatcat:xdjh2kzqdjdeldxl2dwr7riaci
*Feedback*Arc*Set*problem restricted to tournaments is known as the k-*Feedback*Arc*Set*in Tournaments (k-FAST) problem. In this paper we obtain a*linear**vertex**kernel**for*k-FAST. ... Our*kernelization*algorithm solves the problem on a subclass of tournaments in polynomial*time*and uses a known polynomial*time*approximation scheme*for*k-FAST. ... In Section 2, we give some definition and preliminary results regarding*feedback*arc*sets*. In Section 3 we give a*linear**vertex**kernel**for*k-FAST. ...##
###
Kernels for feedback arc set in tournaments

2011
*
Journal of computer and system sciences (Print)
*

The

doi:10.1016/j.jcss.2010.10.001
fatcat:6hmv67xnzvgyjma2y4loaszvvq
*Feedback*Arc*Set*problem restricted to tournaments is known as the k-*Feedback*Arc*Set*in Tournaments (k-FAST) problem. In this paper we obtain a*linear**vertex**kernel**for*k-FAST. ... Our*kernelization*algorithm solves the problem on a subclass of tournaments in polynomial*time*and uses a known polynomial*time*approximation scheme*for*k-FAST. * ... In Section 2, we give some definition and preliminary results regarding*feedback*arc*sets*. In Section 3 we give a*linear**vertex**kernel**for*k-FAST. ...##
###
Fixed-parameter tractability results for full-degree spanning tree and its dual

2009
*
Networks
*

We provide first-

doi:10.1002/net.20353
fatcat:3dufkge6abgxvjkpewufyipqg4
*time*fixed-parameter tractability results*for*the NP-complete problems Maximum Full-Degree Spanning Tree and Minimum-*Vertex**Feedback*Edge*Set*. ...*For*Minimum-*Vertex**Feedback*Edge*Set*the task is to minimize the number of vertices that end up with a reduced degree. ... [1]*for*proving a*linear*-size*kernel**for*Dominating*Set*in planar graphs. ...##
###
Fixed-Parameter Tractability Results for Full-Degree Spanning Tree and Its Dual
[chapter]

2006
*
Lecture Notes in Computer Science
*

We provide first-

doi:10.1007/11847250_19
fatcat:tvodrx6z5beb7kkwvuxipjl6fe
*time*fixed-parameter tractability results*for*the NP-complete problems Maximum Full-Degree Spanning Tree and Minimum-*Vertex**Feedback*Edge*Set*. ...*For*Minimum-*Vertex**Feedback*Edge*Set*the task is to minimize the number of vertices that end up with a reduced degree. ... [1]*for*proving a*linear*-size*kernel**for*Dominating*Set*in planar graphs. ...##
###
New Races in Parameterized Algorithmics
[chapter]

2012
*
Lecture Notes in Computer Science
*

Herein, the attention usually focuses on improving the running

doi:10.1007/978-3-642-32589-2_2
fatcat:gpfsek5febh5rikaagecihqclq
*time*factor exponential in the considered parameter, and, in case of*kernelization*algorithms, to improve the bound on the*kernel*size. ... We discuss several of these aspects and particularly focus on the search*for*"stronger parameterizations" in developing fixed-parameter algorithms. ... We thank André Nichterlein, Manuel Sorge, and Mathias Weller*for*their comments which have improved this article. ...##
###
Parameterized Algorithmics and Computational Experiments for Finding 2-Clubs
[chapter]

2012
*
Lecture Notes in Computer Science
*

On the positive side, we give polynomial-size problem

doi:10.1007/978-3-642-33293-7_22
fatcat:5hbgpg6wuzbcbetfwpivstuxle
*kernels**for*the parameters*feedback*edge*set*size of G and size of a cluster editing*set*of G and present a direct combinatorial algorithm*for*the ... Given an undirected graph G = (V, E) and an integer ≥ 1, the NPhard 2-Club problem asks*for*a*vertex**set*S ⊆ V of size at least such that the subgraph induced by S has diameter at most two. ... A*Linear**Kernel**for*the Parameter*Feedback*Edge*Set*Size A*feedback*edge*set*F of a graph G is an edge*set*whose deletion transforms the graph G into a forest. ...##
###
Parameterized Algorithmics and Computational Experiments for Finding 2-Clubs

2015
*
Journal of Graph Algorithms and Applications
*

On the positive side, we give polynomial-size problem

doi:10.7155/jgaa.00352
fatcat:5xnvb6pycbf2rjuz35ju7p7tgq
*kernels**for*the parameters*feedback*edge*set*size of G and size of a cluster editing*set*of G and present a direct combinatorial algorithm*for*the ... Given an undirected graph G = (V, E) and an integer ≥ 1, the NPhard 2-Club problem asks*for*a*vertex**set*S ⊆ V of size at least such that the subgraph induced by S has diameter at most two. ... A*Linear**Kernel**for*the Parameter*Feedback*Edge*Set*Size A*feedback*edge*set*F of a graph G is an edge*set*whose deletion transforms the graph G into a forest. ...##
###
On tractable cases of Target Set Selection

2012
*
Social Network Analysis and Mining
*

number", "

doi:10.1007/s13278-012-0067-7
fatcat:k2q4nk4qnbatnemcvpvm32tqjq
*vertex*cover number", and "*feedback*edge*set*number" of the underlying graph on the problem's complexity, revealing both tractable and intractable cases. ... TSS can be efficiently solved on graphs with small*feedback*edge*set*number and also turns out to be fixed-parameter tractable when parameterized by the*vertex*cover number, both results contrasting known ... TARGET*SET*SELECTION admits a problem*kernel*of size O(f ), where f denotes the*feedback*edge*set*number. The*kernelization*runs in*linear**time*. ...##
###
On Tractable Cases of Target Set Selection
[chapter]

2010
*
Lecture Notes in Computer Science
*

number", "

doi:10.1007/978-3-642-17517-6_34
fatcat:utuzuybyojah5iljtjbk3j2cuq
*vertex*cover number", and "*feedback*edge*set*number" of the underlying graph on the problem's complexity, revealing both tractable and intractable cases. ... TSS can be efficiently solved on graphs with small*feedback*edge*set*number and also turns out to be fixed-parameter tractable when parameterized by the*vertex*cover number, both results contrasting known ... TARGET*SET*SELECTION admits a problem*kernel*of size O(f ), where f denotes the*feedback*edge*set*number. The*kernelization*runs in*linear**time*. ...##
###
The Power of Data Reduction for Matching
[article]

2017
*
arXiv
*
pre-print

We investigate how

arXiv:1609.08879v2
fatcat:7kxmo2z3nnehlpa5tngr3ziyzy
*linear*-*time*(and almost*linear*-*time*) data reduction (used as preprocessing) can alleviate the situation. More specifically, we focus on (almost)*linear*-*time**kernelization*. ...*For*m-edge and n-*vertex*graphs, it is well-known to be solvable in O(m√(n))*time*; however,*for*several applications this running*time*is still too slow. ... As a warm-up we first show that a subset of our data reduction rules*for*the "*feedback**vertex**set**kernel*" also yields a*linear*-*time*computable*linear*-size*kernel**for*the typically much larger parameter ...##
###
Dynamic Parameterized Problems

2017
*
Algorithmica
*

*For*specific cases of Dynamic Π-Deletion such as Dynamic

*Vertex*Cover and Dynamic

*Feedback*

*Vertex*

*Set*, we describe improved FPT algorithms and give

*linear*

*kernels*. ... Then, we show that Dynamic

*Feedback*

*Vertex*

*Set*admits a randomized algorithm with 1.6667 k n O(1) running

*time*. ... We are also thankful to the reviewers

*for*their suggestions that strengthened the results

*for*Dynamic Π-Deletion. ...

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