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Faster Parameterized Algorithms for Deletion to Split Graphs

Esha Ghosh, Sudeshna Kolay, Mrinal Kumar, Pranabendu Misra, Fahad Panolan, Ashutosh Rai, M. S. Ramanujan
2013 Algorithmica  
In addition, we note that our 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  ... 
doi:10.1007/s00453-013-9837-5 fatcat:eq7mhe7hx5fcfjw2ukkzcebe2m

Faster Parameterized Algorithms for Deletion to Split Graphs [chapter]

Esha Ghosh, Sudeshna Kolay, Mrinal Kumar, Pranabendu Misra, Fahad Panolan, Ashutosh Rai, M. S. Ramanujan
2012 Lecture Notes in Computer Science  
In addition, we note that our 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  ... 
doi:10.1007/978-3-642-31155-0_10 fatcat:ijwle5u57zbcjp43b5lzqxepde

Weakening Covert Networks by Minimizing Inverse Geodesic Length

Haris Aziz, Serge Gaspers, Kamran Najeebullah
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
On the positive side, we design several multivariate 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.  ... 
doi:10.24963/ijcai.2017/108 dblp:conf/ijcai/0001GN17 fatcat:ohovathksveq7h32zhhcc7htmi

Even faster parameterized cluster deletion and cluster editing

Sebastian Böcker, Peter Damaschke
2011 Information Processing Letters  
Even 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".  ... 
doi:10.1016/j.ipl.2011.05.003 fatcat:7gguo5pwgnf3do2vebdlr75rmq

Parameterized Algorithms for (r,l)-Partization

R. Krithika, N. S. Narayanaswamy
2013 Journal of Graph Algorithms and Applications  
Restricted 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  ... 
doi:10.7155/jgaa.00288 fatcat:z4rxo66s7jgx5juiysfmhrmr6y

On the Parameterized Approximability of Contraction to Classes of Chordal Graphs

Spoorthy Gunda, Pallavi Jain, Daniel Lokshtanov, Saket Saurabh, Prafullkumar Tale, Raghu Meka, Jarosław Byrka
2020 International Workshop on Approximation Algorithms for Combinatorial Optimization  
Firstly, we give a (2+ε)-approximate polynomial kernel 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) .  ... 
doi:10.4230/lipics.approx/random.2020.51 dblp:conf/approx/Gunda0L0T20 fatcat:yfp3qh2thrghfgncfl7vv4wmcq

Parameterized Algorithms on Perfect Graphs for deletion to (r,ℓ)-graphs [article]

Sudeshna Kolay and Fahad Panolan and Venkatesh Raman and Saket Saurabh
2015 arXiv   pre-print
It is also known 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.  ... 
arXiv:1512.04200v1 fatcat:itrvcbkukveqbiz4r2tiarpz7u

On 2-Clubs in Graph-Based Data Clustering: Theory and Algorithm Engineering [article]

Aleksander Figiel, Anne-Sophie Himmel, André Nichterlein, Rolf Niedermeier
2020 arXiv   pre-print
kernel when 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.  ... 
arXiv:2006.14972v1 fatcat:pdshakcombchlcmjmxnwnn4s7e

Parameterized complexity of vertex colouring

Leizhen Cai
2003 Discrete Applied Mathematics  
ÿxed k but W [1]-hard 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.  ... 
doi:10.1016/s0166-218x(02)00242-1 fatcat:yjsvum3eijcbfmnqxusumn6kzq

LP can be a cure for Parameterized Problems

N.S. Narayanaswamy, Venkatesh Raman, M.S. Ramanujan, Saket Saurabh, Marc Herbstritt
2012 Symposium on Theoretical Aspects of Computer Science  
Then, using known and new reductions, we give O * (2.6181 k ) 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.  ... 
doi:10.4230/lipics.stacs.2012.338 dblp:conf/stacs/NarayanaswamyRRS12 fatcat:3ing2rm3mjar7ljqroq35jd4sm

Parameterized Algorithms for Deletion to (r,l)-graphs [article]

Sudeshna Kolay, Fahad Panolan
2015 arXiv   pre-print
We do not hope 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.  ... 
arXiv:1504.08120v1 fatcat:wejgpc5ng5ek3kcyeidl6ttcny

Experimental Evaluation of Parameterized Algorithms for Feedback Vertex Set

Krzysztof Kiljan, Marcin Pilipczuk, Marc Herbstritt
2018 Symposium on Experimental and Efficient Algorithms  
Feedback Vertex Set is a classic combinatorial optimization problem that asks 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.  ... 
doi:10.4230/lipics.sea.2018.12 dblp:conf/wea/KiljanP18 fatcat:symgz3xuzfffzphp5jkzox3qwy

Quick Separation in Chordal and Split Graphs

Pranabendu Misra, Fahad Panolan, Ashutosh Rai, Saket Saurabh, Roohani Sharma, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
Towards designing 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.  ... 
doi:10.4230/lipics.mfcs.2020.70 dblp:conf/mfcs/MisraP00S20 fatcat:zvxz7xaj5vairbvhncasrxqze4

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.  ...  We thank Marcin Pilipczuk, William Lochet, and Dekel Tsur for helpful comments. References  ... 
arXiv:2001.06867v2 fatcat:6ogysat6n5drpbxsvs63zjmega

On the Feasibility of Maintenance Algorithms in Dynamic Graphs [article]

Arnaud Casteigts, Bernard Mans, Luke Mathieson
2012 arXiv   pre-print
or 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  ... 
arXiv:1107.2722v4 fatcat:dgnb25gcgzetbdtyadlajgcrlu
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