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An FPT Algorithm for Elimination Distance to Bounded Degree Graphs

2021

They showed that

doi:10.4230/lipics.stacs.2021.5
fatcat:z5kxoecfufcpdjsqammeo7ql3i
*Graph*Isomorphism parameterized by the*elimination**distance**to**bounded**degree**graphs*is fixed-parameter tractable and asked whether determining the*elimination**distance**to*the class of ...*bounded**degree**graphs*is fixed-parameter tractable. ... A second direction is*to*investigate the parameterized complexity of various S TA C S 2 0 2 1 5:10*An**FPT**Algorithm**for**Elimination**Distance**to**Bounded**Degree**Graphs**graphs*problems parameterized by ...##
###
Fixed-Parameter Tractable Distances to Sparse Graph Classes

2016
*
Algorithmica
*

The second shows that determining the

doi:10.1007/s00453-016-0235-7
fatcat:yk3piechqnec5gusen2sl7jp4u
*elimination**distance*of a*graph*G*to*a minor-closed class C is*FPT*. ... We show that*for*various classes C of sparse*graphs*, and several measures of*distance**to*such classes (such as edit*distance*and*elimination**distance*), the problem of determining the*distance*of a given ... Another recently introduced measure is*elimination**distance*, defined in [3] where it was shown that*graph*isomorphism is*FPT*when parameterized by*elimination**distance**to*a class of*graphs*of*bounded*...##
###
Fixed-parameter Tractable Distances to Sparse Graph Classes
[article]

2015
*
arXiv
*
pre-print

The second shows that determining the

arXiv:1502.05910v1
fatcat:uhxviaio4nfo3aahfvdks3eeuq
*elimination**distance*of a*graph*G*to*a minor-closed class C is*FPT*. ... We show that*for*various classes C of sparse*graphs*, and several measures of*distance**to*such classes (such as edit*distance*and*elimination**distance*), the problem of determining the*distance*of a given ... A natural open question raised by these two results is whether*elimination**distance**to*the class of*graphs*of*degree*d is*FPT*. ...##
###
Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree
[chapter]

2014
*
Lecture Notes in Computer Science
*

We establish that

doi:10.1007/978-3-319-13524-3_12
fatcat:elbyocaifvdfrdwxkhj7zdofmq
*graph*canonisation, and thus*graph*isomorphism, is*FPT*when parameterized by*elimination**distance**to**bounded**degree*, extending results of Bouland et al. ... that need*to*be deleted from a*graph**to*place it in some class*for*which efficient*algorithms*are known. ... Corollary 6.8*Graph*Isomorphism is*FPT*parameterized by*elimination**distance**to**bounded**degree*. ...##
###
Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree

2015
*
Algorithmica
*

We establish that

doi:10.1007/s00453-015-0045-3
fatcat:aojf733y7vap5hpms43uhazuwq
*graph*canonisation, and thus*graph*isomorphism, is*FPT*when parameterized by*elimination**distance**to**bounded**degree*, extending results of Bouland et al. ... that need*to*be deleted from a*graph**to*place it in some class*for*which efficient*algorithms*are known. ... Corollary 6.8*Graph*Isomorphism is*FPT*parameterized by*elimination**distance**to**bounded**degree*. ...##
###
Deleting, Eliminating and Decomposing to Hereditary Classes Are All FPT-Equivalent
[article]

2022
*
arXiv
*
pre-print

*For*a

*graph*class H, the

*graph*parameters

*elimination*

*distance*

*to*H (denoted by ed_ H) [Bulian and Dawar, Algorithmica, 2016], and H-treewidth (denoted by tw_ H) [Eiben et al. ... As

*an*example, we prove that

*an*

*FPT*

*algorithm*

*for*the vertex-deletion problem implies a non-uniform

*FPT*

*algorithm*

*for*computing ed_ H and tw_ H. ... In fact, they proved a more general result and obtained the result

*for*

*elimination*

*distance*

*to*

*graphs*of

*bounded*

*degree*as a consequence. ...

##
###
Graph Isomorphism Parameterized by Elimination Distance to Bounded Degree
[article]

2014
*
arXiv
*
pre-print

We establish that

arXiv:1406.4718v2
fatcat:ibwbqostf5cchan4wufjeytsba
*graph*canonisation, and thus*graph*isomorphism, is*FPT*when parameterized by*elimination**distance**to**bounded**degree*, extending results of Bouland et al. (2012). ...*for*which efficient*algorithms*are known. ... Canonisation parameterized by*elimination**distance**to**bounded**degree*In this section we show that*graph*canonisation, and thus*graph*isomorphism, is*FPT*parameterized by*elimination**distance**to**bounded*...##
###
Engineering Exact Quasi-Threshold Editing

2020
*
Symposium on Experimental and Efficient Algorithms
*

*For*the

*FPT*

*algorithm*, we introduce a fast heuristic

*for*computing high-quality lower

*bounds*and

*an*improved branching strategy.

*For*the ILP, we engineer several variants of row generation. ... We evaluate both methods

*for*quasi-threshold editing on a large set of protein similarity

*graphs*.

*For*most instances, our optimizations speed up the

*FPT*

*algorithm*by one

*to*three orders of magnitude. ...

*For*the

*FPT*

*algorithm*, we propose a novel lower

*bound*

*algorithm*based on local search heuristics

*for*independent sets as well as

*an*improved branching strategy. ...

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

2013
*
European journal of combinatorics (Print)
*

We call

doi:10.1016/j.ejc.2012.04.008
fatcat:uzjyjuxec5hvlcep3jsf3mcupu
*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 ...*An*extensive overview of recent advances on this front is presented*for*the Vertex Cover problem. ... As G has treewidth at most k, there is*an**elimination*order of G in which each vertex has*degree*at most k upon*elimination*[8, Section 7] . ...##
###
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number

2009
*
Theory of Computing Systems
*

We do two things: (1) We describe much improved

doi:10.1007/s00224-009-9167-9
fatcat:ezqsz2ggzzgd5iicukjjenzoai
*FPT**algorithms**for*a large number of*graph*problems,*for*input*graphs*G*for*which ml(G) ≤ k, based on the polynomial-time extremal structure theory canonically ...*graphs*of*bounded*max leaf number? ... we get*an*O * (4 k )*FPT**algorithm**for*the Minimum Dominating Set problem,*for**graphs*of max leaf number*bounded*by k. ...##
###
The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number
[chapter]

2007
*
Lecture Notes in Computer Science
*

We do two things: (1) We describe much improved

doi:10.1007/978-3-540-73001-9_28
fatcat:6ctmbq7kgrbfpeer6mpc5pqaja
*FPT**algorithms**for*a large number of*graph*problems,*for*input*graphs*G*for*which ml(G) ≤ k, based on the polynomial-time extremal structure theory canonically ...*graphs*of*bounded*max leaf number? ... we get*an*O * (4 k )*FPT**algorithm**for*the Minimum Dominating Set problem,*for**graphs*of max leaf number*bounded*by k. ...##
###
Solving Routing Problems via Important Cuts
[article]

2022
*
arXiv
*
pre-print

The only known

arXiv:2201.12790v2
fatcat:e3g6w2q5hjdbfhgo43ldiyguei
*FPT**algorithm**for*MV parameterized by p (the same parameter as*for*MSE) was*for*chordal*graphs*(Aoki et al., JCO 2018). We design*an**FPT**algorithm**for*MV on all undirected*graphs*. ... We introduce a novel approach of using important cuts which allowed us*to*design significantly faster fixed-parameter tractable (*FPT*)*algorithms**for*the following routing problems: the Mixed Chinese Postman ...*Algorithm*ABBCP Results of Sections 3 and 4.1 allow us*to*design*an**algorithm**for*solving*Bounded*BCPP. ...##
###
Foreword: Special Issue on IPEC 2014

2016
*
Algorithmica
*

Jannis Bulian and Anuj Dawar consider the

doi:10.1007/s00453-016-0151-x
fatcat:2xhmdtkgtzbbppmbxnhugehgr4
*Graph*Isomorphism problem in*Graph*Isomorphism Parameterized by*Elimination**Distance**to**Bounded**Degree*. ... Arvind and Gaurav Rattan present improved*FPT**algorithm**for*Geometric*Graph*Isomorphism problem, where one is*to*decide whether there is a*distance*preserving bijection between two sets of points in k-dimensional ...##
###
Domination Problems in Nowhere-Dense Classes of Graphs
[article]

2009
*
arXiv
*
pre-print

Our result also establishes that the

arXiv:0907.4283v1
fatcat:apxhpisvb5ew5otmn7mmngpcna
*distance*-d dominating-set problem is*FPT*on classes of*bounded*expansion, answering a question of Nešetřil and Ossona de Mendez. ... This generalises known results about the dominating set problem on H-minor free classes, classes with locally excluded minors and classes of*graphs*of*bounded*expansion. ... If we are not interested in their*distance*-d-version than*an*even simpler*algorithm*than the one presented above can be used*to*show that these problems are in*FPT*on nowhere-dense classes of*graphs*, which ...##
###
Elimination Distance to Bounded Degree on Planar Graphs

2020
*
International Symposium on Mathematical Foundations of Computer Science
*

We study the

doi:10.4230/lipics.mfcs.2020.65
dblp:conf/mfcs/LindermayrSV20
fatcat:q7l6fqaqujhj7kewuxyjrbzg6a
*graph*parameter*elimination**distance**to**bounded**degree*, which was introduced by Bulian and Dawar in their study of the parameterized complexity of the*graph*isomorphism problem. ... function f and constant c whether the*elimination**distance*of G*to*the class of*degree*d*graphs*is at most k. ... Conclusion Our proofs show that all difficulties*for**elimination**distance**to**bounded**degree*arise already in*bounded**degree**graphs*. ...
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