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Faster Parameterized Algorithms for Deletion to Split Graphs

2013
*
Algorithmica
*

In addition, we note that our

doi:10.1007/s00453-013-9837-5
fatcat:eq7mhe7hx5fcfjw2ukkzcebe2m
*algorithm**for**Split*Edge*Deletion*adds*to*the small number of subexponential*parameterized**algorithms*not obtained through bidimensionality, and on general*graphs*. ...*For**Split*Edge*Deletion*, the problem of determining whether there are k edges whose*deletion*results in a*split**graph*, we give an O * (2 O( √ k log k) )*algorithm*. ... We wish*to*thank Venkatesh Raman and Saket Saurabh*for*the insightful discussions which led*to*this work, and the anonymous reviewers*for*the numerous comments towards improving the presentation of the ...##
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Faster Parameterized Algorithms for Deletion to Split Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

In addition, we note that our

doi:10.1007/978-3-642-31155-0_10
fatcat:ijwle5u57zbcjp43b5lzqxepde
*algorithm**for**Split*Edge*Deletion*adds*to*the small number of subexponential*parameterized**algorithms*not obtained through bidimensionality, and on general*graphs*. ...*For**Split*Edge*Deletion*, the problem of determining whether there are k edges whose*deletion*results in a*split**graph*, we give an O * (2 O( √ k log k) )*algorithm*. ... We wish*to*thank Venkatesh Raman and Saket Saurabh*for*the insightful discussions which led*to*this work, and the anonymous reviewers*for*the numerous comments towards improving the presentation of the ...##
###
Weakening Covert Networks by Minimizing Inverse Geodesic Length

2017
*
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
*

On the positive side, we design several multivariate

doi:10.24963/ijcai.2017/108
dblp:conf/ijcai/0001GN17
fatcat:ohovathksveq7h32zhhcc7htmi
*algorithms**for*the problem. Our main result is an*algorithm**for*MinIGL*parameterized*by the twin cover number. ... The problem is NP-complete even if $T=0$ and remains both NP-complete and $W[1]$-hard*for*parameter $k$ on bipartite and on*split**graphs*. ... However, we give a*faster**algorithm**for*this parameter. We also provide an FPT*algorithm**parameterized*by neighborhood diversity and the*deletion*budget combined. ...##
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Even faster parameterized cluster deletion and cluster editing

2011
*
Information Processing Letters
*

Even

doi:10.1016/j.ipl.2011.05.003
fatcat:7gguo5pwgnf3do2vebdlr75rmq
*faster**parameterized*cluster*deletion*and cluster editing. ... As this idea is simple and versatile, it may lead*to*improvements*for*several other*parameterized**graph*problems. ... Acknowledgment The second author has been supported by the Swedish Research Council (Vetenskapsrådet), grant 2007-6437, "Combinatorial inference*algorithms*-*parameterization*and clustering". ...##
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Parameterized Algorithms for (r,l)-Partization

2013
*
Journal of Graph Algorithms and Applications
*

Restricted

doi:10.7155/jgaa.00288
fatcat:z4rxo66s7jgx5juiysfmhrmr6y
*to*perfect*graphs*and*split**graphs*, we describe sequacious fixed-parameter tractability results*for*(r, 0)-Partization,*parameterized*by k and r. ...*For*(r, l)-Partization where r + l = 2, we describe an O * (2 k )*algorithm**for*perfect*graphs*. ... Acknowledgements We thank Venkatesh Raman*for*pointing out that our OCT*algorithm**for*perfect*graphs*can be extended*to*Bicochromatization and bringing the*Split**Deletion**algorithm*in [13]*to*our knowledge ...##
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On the Parameterized Approximability of Contraction to Classes of Chordal Graphs

2020
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

Firstly, we give a (2+ε)-approximate polynomial kernel

doi:10.4230/lipics.approx/random.2020.51
dblp:conf/approx/Gunda0L0T20
fatcat:yfp3qh2thrghfgncfl7vv4wmcq
*for**Split*Contraction (which also implies a factor (2+ε)-FPT-approximation*algorithm**for**Split*Contraction). ... Furthermore, we show that, assuming Gap-ETH, there is no (5/4-δ)-FPT-approximation*algorithm**for**Split*Contraction. Here, ε, δ > 0 are fixed constants. - Chordal Contraction is known*to*be W[2]-Hard. ... The*algorithm*returns the reduced instance as (1 + )-lossy kernel*for*(G, k) . ...##
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Parameterized Algorithms on Perfect Graphs for deletion to (r,ℓ)-graphs
[article]

2015
*
arXiv
*
pre-print

It is also known

arXiv:1512.04200v1
fatcat:itrvcbkukveqbiz4r2tiarpz7u
*to*be fixed-parameter tractable (FPT) on perfect*graphs*when*parameterized*by r and ℓ. ...*For*fixed integers r,ℓ≥ 0, a*graph*G is called an (r,ℓ)-*graph*if the vertex set V(G) can be partitioned into r independent sets and ℓ cliques. ...*To*arrive at the kernelization*algorithm*, we consider a slightly larger class of*graphs*called (r, ℓ)-*split**graphs*. ...##
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On 2-Clubs in Graph-Based Data Clustering: Theory and Algorithm Engineering
[article]

2020
*
arXiv
*
pre-print

kernel when

arXiv:2006.14972v1
fatcat:pdshakcombchlcmjmxnwnn4s7e
*parameterized*by the number of vertex*deletions*. ... Editing a*graph*into a disjoint union of clusters is a standard optimization task in*graph*-based data clustering. ... This is likely due*to*the minimum 2-club vertex*deletion*set size (the parameter in our FPT-*algorithm*) on these*graphs*being smaller than*for*Bio33. ...##
###
Parameterized complexity of vertex colouring

2003
*
Discrete Applied Mathematics
*

ÿxed k but W [1]-hard

doi:10.1016/s0166-218x(02)00242-1
fatcat:yjsvum3eijcbfmnqxusumn6kzq
*for**split*+ kv*graphs*. ... In particular, it is shown that the vertex colouring problem is ÿxed-parameter tractable (linear time*for*each ÿxed k)*for**split*+ ke*graphs*and*split*− ke*graphs*, solvable in polynomial time*for*each ... Acknowledgements The author thanks the referees*for*constructive suggestions. ...##
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LP can be a cure for Parameterized Problems

2012
*
Symposium on Theoretical Aspects of Computer Science
*

Then, using known and new reductions, we give O * (2.6181 k )

doi:10.4230/lipics.stacs.2012.338
dblp:conf/stacs/NarayanaswamyRRS12
fatcat:3ing2rm3mjar7ljqroq35jd4sm
*algorithms**for*the*parameterized*versions of Above Guarantee Vertex Cover, Odd Cycle Transversal,*Split*Vertex*Deletion*and Almost 2-SAT, and ... an O * (1.6181 k )*algorithm**for*Konig Vertex*Deletion*, Vertex Cover Param by OCT and Vertex Cover Param by KVD. ... Recently, in [13] , a significantly*faster**algorithm**for*Vertex Cover above LP, running in time O * (2.3146 k ), has been obtained. ...##
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Parameterized Algorithms for Deletion to (r,l)-graphs
[article]

2015
*
arXiv
*
pre-print

We do not hope

arXiv:1504.08120v1
fatcat:wejgpc5ng5ek3kcyeidl6ttcny
*to*get*parameterized**algorithms**for*either Vertex (r,ℓ)-Partization or Edge (r,ℓ)-Partization when either of r or ℓ is at least 3 as the recognition problem itself is NP-complete. ... These problems generalize well studied problems such as Odd Cycle Transversal, Edge Odd Cycle Transversal,*Split*Vertex*Deletion*and*Split*Edge*Deletion*. ... Approximation*algorithms**for*Vertex*Deletion**to*(r, ℓ)-*graphs*In this section we give a polynomial time approximation*algorithm**for*Vertex (2, 2)-Partization. ...##
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Experimental Evaluation of Parameterized Algorithms for Feedback Vertex Set

2018
*
Symposium on Experimental and Efficient Algorithms
*

Feedback Vertex Set is a classic combinatorial optimization problem that asks

doi:10.4230/lipics.sea.2018.12
dblp:conf/wea/KiljanP18
fatcat:symgz3xuzfffzphp5jkzox3qwy
*for*a minimum set of vertices in a given*graph*whose*deletion*makes the*graph*acyclic. ... ACM Subject Classification Theory of computation →*Parameterized*complexity and exact*algorithms*, Theory of computation →*Graph**algorithms*analysis Keywords and phrases Empirical Evaluation of*Algorithms*... Introduction The Feedback Vertex Set problem asks*to**delete*from a given*graph*a minimum number of vertices*to*make it acyclic. ...##
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Quick Separation in Chordal and Split Graphs

2020
*
International Symposium on Mathematical Foundations of Computer Science
*

Towards designing

doi:10.4230/lipics.mfcs.2020.70
dblp:conf/mfcs/MisraP00S20
fatcat:zvxz7xaj5vairbvhncasrxqze4
*faster*FPT*algorithms*and polynomial kernels*for*the above mentioned problems, we study them on chordal and*split**graphs*. ... Hence Multicut on chordal*graphs**parameterized*by the number of terminals is in XP. 3) Multicut on*split**graphs*can be solved in time min {𝒪(1.2738^k + kn+𝓁(n+m), 𝒪(2^{𝓁} ⋅ 𝓁 ⋅ (n+m))}. ... We also consider UMC on*split**graphs*and design an FPT*algorithm**for*it*parameterized*by . Let us note that, while UMC can be easily reduced*to*MC, the reduction does not produce a*split**graph*. ...##
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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

arXiv:2001.06867v2
fatcat:6ogysat6n5drpbxsvs63zjmega
*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. ... We thank Marcin Pilipczuk, William Lochet, and Dekel Tsur*for*helpful comments. References ...##
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On the Feasibility of Maintenance Algorithms in Dynamic Graphs
[article]

2012
*
arXiv
*
pre-print

or

arXiv:1107.2722v4
fatcat:dgnb25gcgzetbdtyadlajgcrlu
*to*adapt the known solution on the prior*graph**to*quickly provide a solution of guaranteed quality*for*the changed*graph*? ... Near ubiquitous mobile computing has led*to*intense interest in dynamic*graph*theory. This provides a new and challenging setting*for**algorithmics*and complexity theory. ... In this case we would ideally like an*algorithm*that can exploit the known solution*to*the previous*graph*, which is somewhat similar*to*the current*graph*,*to*produce a solution*for*the current*graph*that ...
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