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The parameterized complexity of k-edge induced subgraphs [article]

Bingkai Lin, Yijia Chen
2012 arXiv   pre-print
Hence, the k-edge induced subgraph problem is one of the rare known examples in parameterized complexity that are easy for decision while hard for counting.  ...  We prove that finding a k-edge induced subgraph is fixed-parameter tractable, thereby answering an open problem of Leizhen Cai.  ...  We thank Leizhen Cai for bringing the problem p-Edge-Induced-Subgraph to our attention, and Jörg Flum for comments on earlier versions of this paper.  ... 
arXiv:1105.0477v3 fatcat:qrkw5khxyjfwnaduywsqq7ghoa

The Parameterized Complexity of k-Edge Induced Subgraphs [chapter]

Bingkai Lin, Yijia Chen
2012 Lecture Notes in Computer Science  
Hence, the k-edge induced subgraph problem is one of the very few known examples in parameterized complexity that are easy for decision while hard for counting. p-Edge-Induced-Subgraph Instance: A graph  ...  Parameter: k. Problem: Decide whether G contains a k-edge induced subgraph. As the main result of our paper, we show that p-Edge-Induced-Subgraph is fixed-parameter tractable.  ...  Acknowledgement We thank Leizhen Cai for bringing the problem p-Edge-Induced-Subgraph to our attention, and Jörg Flum for comments on earlier versions of this paper.  ... 
doi:10.1007/978-3-642-31594-7_54 fatcat:beqyvt72mng7faaf4z2ykmlffq

Parameterized complexity of connected even/odd subgraph problems

Fedor V. Fomin, Petr A. Golovach
2014 Journal of computer and system sciences (Print)  
They succeed to establish the parameterized complexity of all cases except two, when we ask about a connected k-edge subgraph with all vertices of odd degrees, the problem known as k-Edge Connected Odd  ...  Subgraph; and a connected k-vertex induced subgraph with all vertices of even degrees, the problem known as k-Vertex Eulerian Subgraph.  ...  The authors are grateful to the anonymous referees for their constructive suggestions and remarks.  ... 
doi:10.1016/j.jcss.2013.07.002 fatcat:mdxidlkmdvhmvcvneg7rbg2i7y

On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism [article]

Faisal N. Abu-Khzam, Édouard Bonnet, Florian Sikora
2017 arXiv   pre-print
In the Maximum Common Induced Subgraph problem (henceforth MCIS), given two graphs G_1 and G_2, one looks for a graph with the maximum number of vertices being both an induced subgraph of G_1 and G_2.  ...  MCIS is among the most studied classical NP-hard problems. It remains NP-hard on many graph classes including forests. In this paper, we study the parameterized complexity of MCIS.  ...  Parameterized Complexity with respect to the natural parameter We study the parameterized complexity of Induced Subgraph Isomorphism, Maximum Common Induced Subgraph, Induced Connected Subgraph Isomorphism  ... 
arXiv:1412.1261v2 fatcat:ownbquhznvcrnmz4uthnys5o3m

On the Complexity of Various Parameterizations of Common Induced Subgraph Isomorphism [chapter]

Faisal N. Abu-Khzam, Édouard Bonnet, Florian Sikora
2015 Lecture Notes in Computer Science  
In the Maximum Common Induced Subgraph problem (henceforth MCIS), given two graphs G 1 and G 2 , one looks for a graph with the maximum number of vertices being both an induced subgraph of G 1 and G 2  ...  MCIS is among the most studied classical NP-hard problems. It remains NP-hard on many graph classes including forests. In this paper, we study the parameterized complexity of MCIS.  ...  Parameterized Complexity with respect to the natural parameter We study the parameterized complexity of Induced Subgraph Isomorphism, Maximum Common Induced Subgraph, Induced Connected Subgraph Isomorphism  ... 
doi:10.1007/978-3-319-19315-1_1 fatcat:knzdi3nve5ao7kvxr7ubulpdnq

On the complexity of various parameterizations of common induced subgraph isomorphism

Faisal N. Abu-Khzam, Édouard Bonnet, Florian Sikora
2017 Theoretical Computer Science  
MCIS remains NP-hard on many graph classes including bipartite graphs, planar graphs and k-trees. Little is known, however, about the parameterized complexity of the problem.  ...  Maximum Common Induced Subgraph (henceforth MCIS) is among the most studied classical NP-hard problems.  ...  Parameterized complexity.  ... 
doi:10.1016/j.tcs.2017.07.010 fatcat:dabbehi67bcwlmjt2ygu67b5dy

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
At the same time, most of the previous work in parameterized streaming complexity was restricted to the EA (edge arrival) or DEA (dynamic edge arrival) models.  ...  Transversal, Triangle Deletion or the more general F-Subgraph Deletion when parameterized by solution size k.  ...  Our study also compared the parameterized streaming complexity of several graph deletion problems in the different streaming models.  ... 
arXiv:1906.05458v2 fatcat:cmne5hu34rgohatqv2il7kayay

Maximum common subgraph: some upper bound and lower bound results

Xiuzhen Huang, Jing Lai, Steven F Jennings
2006 BMC Bioinformatics  
Results: Based on current research in the area of parameterized computation, we derive a new lower bound for the exact algorithms of the maximum common induced subgraph of two graphs which is the best  ...  Among the many different variants of the maximum common subgraph problem, the maximum common induced subgraph of two graphs is of special interest.  ...  Let E be the set of compatible edges. A k-clique in the new graph G can be interpreted as a matching between two induced k-node subgraphs.  ... 
doi:10.1186/1471-2105-7-s4-s6 pmid:17217524 pmcid:PMC1780128 fatcat:cns452toozfv7o635fytv3qfwy

Parameterized complexity of finding subgraphs with hereditary properties

Subhash Khot, Venkatesh Raman
2002 Theoretical Computer Science  
there k vertices of G that induce a subgraph with property ?  ...  We consider the parameterized complexity of the following problem under the framework introduced by Downey and Fellows: Given a graph G, an integer parameter k and a nontrivial hereditary property , are  ...  Acknowledgements We thank Mike Fellows for his comments on an earlier draft of the paper.  ... 
doi:10.1016/s0304-3975(01)00414-5 fatcat:ai4tsnt3n5e3tenxbt7iqsxuoi

The Complexity of König Subgraph Problems and Above-Guarantee Vertex Cover

Sounaka Mishra, Venkatesh Raman, Saket Saurabh, Somnath Sikdar, C. R. Subramanian
2010 Algorithmica  
2. does there exist a set of k vertices (edges) that induce a König-Egerváry subgraph?  ...  Further, while studying the parameterized complexity of the problem of deleting k vertices to obtain a König-Egerváry graph, we show a number of interesting structural results on matchings and vertex covers  ...  The Induced König Subgraph Problem In this section we deal with the parameterized complexity and approximability of the vertex and edge versions of the Induced König Subgraph problem.  ... 
doi:10.1007/s00453-010-9412-2 fatcat:lykslhuxpjavvpplwhov2b6neq

Subexponential Parameterized Algorithms and Kernelization on Almost Chordal Graphs

Fedor V. Fomin, Petr A. Golovach, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
induced planar subgraph.  ...  We study algorithmic properties of the graph class Chordal-ke, that is, graphs that can be turned into a chordal graph by adding at most k edges or, equivalently, the class of graphs of fill-in at most  ...  Acknowledgements We thank Torstein Strømme, Daniel Lokshtanov, and Pranabendu Misra for fruitful discussions on the topic of this paper.  ... 
doi:10.4230/lipics.esa.2020.49 dblp:conf/esa/FominG20a fatcat:dh4jo3kb5rc3xgw7rqfted5doi

Parameterized Aspects of Strong Subgraph Closure

Petr A. Golovach, Pinar Heggernes, Athanasios L. Konstantinidis, Paloma T. Lima, Charis Papadopoulos
2020 Algorithmica  
Motivated by the role of triadic closures in social networks, and the importance of finding a maximum subgraph avoiding a fixed pattern, we introduce and initiate the parameterized study  ...  The parameterized complexity of F -free Edge Deletion has been studied extensively when parameterized by , the number of removed edges.  ...  The task is to decide whether we can select at least k edges of G and mark them as strong, in the following way: whenever the subgraph of G spanned by the strong edges contains an induced subgraph isomorphic  ... 
doi:10.1007/s00453-020-00684-9 fatcat:nhbdwiiu35hndapxu3wdxes7ou

On parameterized complexity of the Multi-MCS problem

Wenbin Chen, Matthew C. Schmidt, Nagiza F. Samatova
2009 Theoretical Computer Science  
k are the size of the maximum common subgraph and the number of multiple graphs, respectively.  ...  On the basis of the framework of parameterized complexity theory, we derive the parameterized complexity of Multi-MCS for various parameters for different classes of graphs.  ...  These are analogous to the well-known Maximum Common Induced Subgraph and Maximum Common Edge Subgraph problems for two graphs (MCIS and MCES, repectively).  ... 
doi:10.1016/j.tcs.2008.12.060 fatcat:2xik7aabnrbgbhxb5po7u4gp7m

Parameterized complexity of even/odd subgraph problems

Leizhen Cai, Boting Yang
2011 Journal of Discrete Algorithms  
We study the parameterized complexity of the problems of determining whether a graph contains a k-edge subgraph (k-vertex induced subgraph) that is a Π -graph for Π -graphs being one of the following four  ...  We also consider the parameterized complexity of their parametric dual problems. For these sixteen problems, we show that eight of them are fixed parameter tractable and four are W[1]-hard.  ...  Acknowledgements The authors would like to thank the anonymous referees for their valuable comments and suggestions.  ... 
doi:10.1016/j.jda.2011.03.004 fatcat:zxraxj2ysnhyvanrm56ejxsmp4

Parameterized Complexity of Even/Odd Subgraph Problems [chapter]

Leizhen Cai, Boting Yang
2010 Lecture Notes in Computer Science  
We study the parameterized complexity of the problems of determining whether a graph contains a k-edge subgraph (k-vertex induced subgraph) that is a Π -graph for Π -graphs being one of the following four  ...  We also consider the parameterized complexity of their parametric dual problems. For these sixteen problems, we show that eight of them are fixed parameter tractable and four are W[1]-hard.  ...  Acknowledgements The authors would like to thank the anonymous referees for their valuable comments and suggestions.  ... 
doi:10.1007/978-3-642-13073-1_9 fatcat:q4yz7vmmfbf5volu5d236ddqjy
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