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On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem

Robert Ganian, Fabian Klute, Sebastian Ordyniak
2020 Algorithmica  
We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound.  ...  We first show that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters such as the feedback vertex set number, pathwidth, treedepth, and even the size of  ...  To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.  ... 
doi:10.1007/s00453-020-00758-8 fatcat:hm2hkvmehrcxzirytp5oqmae6u

New Races in Parameterized Algorithmics [chapter]

Christian Komusiewicz, Rolf Niedermeier
2012 Lecture Notes in Computer Science  
Herein, the attention usually focuses on improving the running 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.  ...  For vertex cover, one such parameterization is "parameterization above matching lower bound", that is, one asks whether there is a vertex cover of size at most + k, where is the size of a maximum matching  ... 
doi:10.1007/978-3-642-32589-2_2 fatcat:gpfsek5febh5rikaagecihqclq

Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, Andrew Van Der Poel, Michael Wagner
2019 European Symposium on Algorithms  
The idea is to edit a given graph via vertex-or edge-deletions to put the graph into an algorithmically tractable class, apply known approximation algorithms for that class, and then lift the solution  ...  We give a general characterization of when an optimization problem is amenable to this approach, and show that it includes many well-studied graph problems, such as Independent Set, Vertex Cover, Feedback  ...  on the manuscript.  ... 
doi:10.4230/lipics.esa.2019.37 dblp:conf/esa/DemaineGKLLSVP19 fatcat:sa6gr2pm3rggpdb5pehdxtmk6e

Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics [chapter]

Christian Komusiewicz, André Nichterlein, Rolf Niedermeier
2016 Lecture Notes in Computer Science  
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain  ...  For example, the Cluster Deletion problem asks to delete as few edges as possible such that the resulting graph is a disjoint union of cliques.  ...  An example for above-lower bound parameterization is Vertex Cover. One lower bound on the size of a Vertex Cover is the value of a linear programming (LP) relaxation.  ... 
doi:10.1007/978-3-662-53174-7_1 fatcat:kegsdk75mncyhjecqz3ztmtffa

Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics [article]

Christian Komusiewicz, André Nichterlein, Rolf Niedermeier
2016 arXiv   pre-print
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain  ...  For example, the Cluster Deletion problem asks to delete as few edges as possible such that the resulting graph is a disjoint union of cliques.  ...  An example for above-lower bound parameterization is Vertex Cover. One lower bound on the size of a Vertex Cover is the value ℓ of a linear programming (LP) relaxation.  ... 
arXiv:1606.03268v1 fatcat:6ucc6vh32rfajofrbdsxtcpznq

Revisiting Connected Vertex Cover: FPT Algorithms and Lossy Kernels

R. Krithika, Diptapriyo Majumdar, Venkatesh Raman
2018 Theory of Computing Systems  
The CONNECTED VERTEX COVER problem asks for a vertex cover in a graph that induces a connected subgraph.  ...  The parameters we consider are the sizes of a split deletion set, clique deletion set, clique cover, cluster deletion set and chordal deletion set.  ...  The pair consisting of a decision problem and a parameterization is called a parameterized problem. A common parameter is a bound on the size of an optimum solution for the problem instance.  ... 
doi:10.1007/s00224-017-9837-y fatcat:qo4mohfk7je5rgl6zhxwjk3z4a

Structural Parameterization for Graph Deletion Problems over Data Streams [article]

Arijit Bishnu and Arijit Ghosh and Sudeshna Kolay and Gopinath Mishra and Saket Saurabh
2019 arXiv   pre-print
We focus on the vertex cover size K as the parameter for the parameterized graph deletion problems we consider.  ...  Most of the graph problems that do have streaming algorithms of the above nature are ones where localized checking is required, like Vertex Cover or Maximum Matching parameterized by the size k of the  ...  Conclusion In this paper, we initiate the study of parameterized streaming complexity with structural parameters for graph deletion problems.  ... 
arXiv:1906.05458v2 fatcat:cmne5hu34rgohatqv2il7kayay

On Bounded-Degree Vertex Deletion parameterized by treewidth

Nadja Betzler, Robert Bredereck, Rolf Niedermeier, Johannes Uhlmann
2012 Discrete Applied Mathematics  
On the positive side, we show that Bounded-Degree Vertex Deletion becomes fixed-parameter tractable when parameterized by the combined parameter treewidth and number of vertices to delete, and when parametrized  ...  Given an undirected graph G and an integer d ≥ 0, the NP-hard Bounded-Degree Vertex Deletion problem asks to delete as few vertices as possible from G such that the resulting graph has maximum vertex degree  ...  Acknowledgments The first and second author were supported by the DFG, research project PAWS, NI 369/10. The fourth author was supported by the DFG, research project PABI, NI 369/7.  ... 
doi:10.1016/j.dam.2011.08.013 fatcat:he5hhus65zggbemzi2qlcukfhi

A survey of parameterized algorithms and the complexity of edge modification [article]

Christophe Crespelle, Pål Grønås Drange, Fedor V. Fomin, Petr A. Golovach
2020 arXiv   pre-print
The survey provides an overview of the developing area of parameterized algorithms for graph modification problems.  ...  We concentrate on edge modification problems, where the task is to change a small number of adjacencies in a graph in order to satisfy some required property.  ...  The variant of DCE(S) with degree lists of size one, where S ⊆ {vertex deletion, edge deletion} and where we are given separate bounds k v and k e for the number of vertex and edge deletions respectively  ... 
arXiv:2001.06867v2 fatcat:6ogysat6n5drpbxsvs63zjmega

A Parameterized Algorithm for Bounded-Degree Vertex Deletion [chapter]

Mingyu Xiao
2016 Lecture Notes in Computer Science  
The d-bounded-degree vertex deletion problem, to delete at most k vertices in a given graph to make the maximum degree of the remaining graph at most d, finds applications in computational biology, social  ...  It can be regarded as a special case of the (d+2)-hitting set problem and generates the famous vertex cover problem. The d-bounded-degree vertex deletion problem is NP-hard for each fixed d≥ 0.  ...  Introduction The d-bounded-degree vertex deletion problem is also extensively studied in theory, especially in parameterized complexity.  ... 
doi:10.1007/978-3-319-42634-1_7 fatcat:naaiui3lofhz3pzoq42a5kh7fu

Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity

Michael R. Fellows, Bart M.P. Jansen, Frances Rosamond
2013 European journal of combinatorics (Print)  
An extensive overview of recent advances on this front is presented for the Vertex Cover problem.  ...  We call for a new type of race in parameterized analysis, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or  ...  the parameterization by a promised bound on the vertex-deletion distance to a perfect graph.  ... 
doi:10.1016/j.ejc.2012.04.008 fatcat:uzjyjuxec5hvlcep3jsf3mcupu

Polynomial Kernels for Hitting Forbidden Minors under Structural Parameterizations

Bart M. P. Jansen, Astrid Pieterse, Michael Wagner
2018 European Symposium on Algorithms  
Motivated by several impossibility results, we parameterize the F-Deletion problem by the size of a vertex modulator whose removal results in a graph of constant treedepth η.  ...  We prove that for each set F of connected graphs and constant η, the F-Deletion problem parameterized by the size of a treedepth-η modulator has a polynomial kernel.  ...  The degree of the polynomial in the kernel size bound grows very quickly with η. We prove that this is unavoidable, even for the simplest case of Vertex Cover. Theorem 2 ( ).  ... 
doi:10.4230/lipics.esa.2018.48 dblp:conf/esa/JansenP18 fatcat:af55jmsen5hwpevlhjcb477i6u

Parameterized Inapproximability of Degree Anonymization [chapter]

Cristina Bazgan, André Nichterlein
2014 Lecture Notes in Computer Science  
The Degree Anonymity problem arises in the context of combinatorial graph anonymization.  ...  Complementing recent investigations on its computational complexity, we show that this problem is very hard when studied from the viewpoints of approximation as well as parameterized approximation.  ...  the last block of degree n contains exactly one vertex.  ... 
doi:10.1007/978-3-319-13524-3_7 fatcat:pimnjksrmvbytovvka52nvobii

A Structural View on Parameterizing Problems: Distance from Triviality [chapter]

Jiong Guo, Falk Hüffner, Rolf Niedermeier
2004 Lecture Notes in Computer Science  
Based on a series of known and new examples, we propose the generalized setting of "distance from triviality" measurement as a reasonable and prospective way of determining useful structural problem parameters  ...  The underlying idea is to consider tractable special cases of generally hard problems and to introduce parameters that measure the distance from these special cases.  ...  A different way of parameterizing Vertex Cover is to consider the structure of the input graph.  ... 
doi:10.1007/978-3-540-28639-4_15 fatcat:2oemfxdjpre35b4fou62izyxgu

Parameterized Streaming Algorithms for Vertex Cover [article]

Rajesh Chitnis, Graham Cormode, MohammadTaghi Hajiaghayi, Morteza Monemizadeh
2014 arXiv   pre-print
By combining kernelization techniques with randomized sketch structures, we obtain the first streaming algorithms for the parameterized versions of the Vertex Cover problem.  ...  In each of these three models we are able to design parameterized streaming algorithms for the Vertex Cover problem.  ...  We thank Catalin Tiseanu for some useful discussions regarding the Feedback Vertex Set problem.  ... 
arXiv:1405.0093v2 fatcat:4mqzunoomvdahi3kbssuvf7cjy
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