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On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem

2020
*
Algorithmica
*

We study

doi:10.1007/s00453-020-00758-8
fatcat:hm2hkvmehrcxzirytp5oqmae6u
*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/. ...##
###
New Races in Parameterized Algorithmics
[chapter]

2012
*
Lecture Notes in Computer Science
*

Herein,

doi:10.1007/978-3-642-32589-2_2
fatcat:gpfsek5febh5rikaagecihqclq
*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 ...##
###
Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

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. ...

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

2016
*
Lecture Notes in Computer Science
*

In graph modification

doi:10.1007/978-3-662-53174-7_1
fatcat:kegsdk75mncyhjecqz3ztmtffa
*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. ...##
###
Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics
[article]

2016
*
arXiv
*
pre-print

In graph modification

arXiv:1606.03268v1
fatcat:6ucc6vh32rfajofrbdsxtcpznq
*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. ...##
###
Revisiting Connected Vertex Cover: FPT Algorithms and Lossy Kernels

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. ...

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

2019
*
arXiv
*
pre-print

We focus

arXiv:1906.05458v2
fatcat:cmne5hu34rgohatqv2il7kayay
*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*. ...##
###
On Bounded-Degree Vertex Deletion parameterized by treewidth

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. ...

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

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 ...

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

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. ...

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

2013
*
European journal of combinatorics (Print)
*

An extensive overview

doi:10.1016/j.ejc.2012.04.008
fatcat:uzjyjuxec5hvlcep3jsf3mcupu
*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. ...##
###
Polynomial Kernels for Hitting Forbidden Minors under Structural Parameterizations

2018
*
European Symposium on Algorithms
*

Motivated by several impossibility results, we

doi:10.4230/lipics.esa.2018.48
dblp:conf/esa/JansenP18
fatcat:af55jmsen5hwpevlhjcb477i6u
*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 ( ). ...##
###
Parameterized Inapproximability of Degree Anonymization
[chapter]

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*. ...

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

2004
*
Lecture Notes in Computer Science
*

Based

doi:10.1007/978-3-540-28639-4_15
fatcat:2oemfxdjpre35b4fou62izyxgu
*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. ...##
###
Parameterized Streaming Algorithms for Vertex Cover
[article]

2014
*
arXiv
*
pre-print

By combining kernelization techniques with randomized sketch

arXiv:1405.0093v2
fatcat:4mqzunoomvdahi3kbssuvf7cjy
*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*. ...
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