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Faster fixed parameter tractable algorithms for finding feedback vertex sets

Venkatesh Raman, Saket Saurabh, C. R. Subramanian
2006 ACM Transactions on Algorithms  
We also investigate the fixed parameter complexity of weighted feedback vertex set problem in weighted undirected graphs.  ...  A feedback vertex set (fvs) of a graph is a set of vertices whose removal results in an acyclic graph.  ...  Paulraja for fruitful discussions and comments on earlier drafts of the article, and Santosh Vempala for suggesting the direction for generalization in Theorem 3.  ... 
doi:10.1145/1159892.1159898 fatcat:yr2r4tetjffbbcxh5ug5lmmvwq

Faster Fixed Parameter Tractable Algorithms for Undirected Feedback Vertex Set [chapter]

Venkatesh Raman, Saket Saurabh, C. R. Subramanian
2002 Lecture Notes in Computer Science  
We also investigate the fixed parameter complexity of weighted feedback vertex set problem in weighted undirected graphs.  ...  A feedback vertex set (fvs) of a graph is a set of vertices whose removal results in an acyclic graph.  ...  Paulraja for fruitful discussions and comments on earlier drafts of the article, and Santosh Vempala for suggesting the direction for generalization in Theorem 3.  ... 
doi:10.1007/3-540-36136-7_22 fatcat:x3msdxladjfl7npwsi5zzxzn5y

New Races in Parameterized Algorithmics [chapter]

Christian Komusiewicz, Rolf Niedermeier
2012 Lecture Notes in Computer Science  
Once having classified an NP-hard problem fixed-parameter tractable with respect to a certain parameter, the race for the most efficient fixed-parameter algorithm starts.  ...  We discuss several of these aspects and particularly focus on the search for "stronger parameterizations" in developing fixed-parameter algorithms.  ...  We thank André Nichterlein, Manuel Sorge, and Mathias Weller for their comments which have improved this article.  ... 
doi:10.1007/978-3-642-32589-2_2 fatcat:gpfsek5febh5rikaagecihqclq

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

Christian Komusiewicz, André Nichterlein, Rolf Niedermeier
2016 Lecture Notes in Computer Science  
We discuss several fruitful interactions between the development of fixed-parameter algorithms and the design of heuristics for graph modification problems, featuring quite different aspects of mutual  ...  Typically, graph modification problems are NP-hard, making them natural candidates for parameterized complexity studies.  ...  We are grateful to Till Fluschnik and Vincent Froese for feedback to our manuscript.  ... 
doi:10.1007/978-3-662-53174-7_1 fatcat:kegsdk75mncyhjecqz3ztmtffa

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

Christian Komusiewicz, André Nichterlein, Rolf Niedermeier
2016 arXiv   pre-print
We discuss several fruitful interactions between the development of fixed-parameter algorithms and the design of heuristics for graph modification problems, featuring quite different aspects of mutual  ...  Typically, graph modification problems are NP-hard, making them natural candidates for parameterized complexity studies.  ...  We are grateful to Till Fluschnik and Vincent Froese for feedback to our manuscript.  ... 
arXiv:1606.03268v1 fatcat:6ucc6vh32rfajofrbdsxtcpznq

Parameterizing above or below guaranteed values

Meena Mahajan, Venkatesh Raman, Somnath Sikdar
2009 Journal of computer and system sciences (Print)  
is fixed-parameter tractable.  ...  We show that if we parameterize "sufficiently" above or below the tight bounds, then these parameterized versions are not fixed-parameter tractable unless P = NP, for a subclass of NP-optimization problems  ...  We note that this problem is fixed-parameter tractable by a parameter-preserving reduction to a weighted variant of Directed Feedback Vertex Set, where the vertices have weights and one has to decide whether  ... 
doi:10.1016/j.jcss.2008.08.004 fatcat:kxs4flhmengrxbougyjbwh4xla

Fixed-parameter tractability results for feedback set problems in tournaments

Michael Dom, Jiong Guo, Falk Hüffner, Rolf Niedermeier, Anke Truss
2010 Journal of Discrete Algorithms  
Using our parameterized algorithm for Feedback Vertex Set in tournaments, we also give an exact (not parameterized) algorithm for it running in O (1.709 n ) time, where n is the number of input graph vertices  ...  We show that Feedback Vertex Set in tournaments (FVST) is amenable to the novel iterative compression technique, and we provide a depth-bounded search tree for Feedback Arc Set in bipartite tournaments  ...  Following the same approach, we derive a fixed-parameter algorithm for Feedback Arc Set in bipartite tournaments (FASBT).  ... 
doi:10.1016/j.jda.2009.08.001 fatcat:qiuhaocrfrcp7aqsbcp3onvjd4

Fixed-Parameter Tractability Results for Feedback Set Problems in Tournaments [chapter]

Michael Dom, Jiong Guo, Falk Hüffner, Rolf Niedermeier, Anke Truß
2006 Lecture Notes in Computer Science  
Using our parameterized algorithm for Feedback Vertex Set in tournaments, we also give an exact (not parameterized) algorithm for it running in O (1.709 n ) time, where n is the number of input graph vertices  ...  We show that Feedback Vertex Set in tournaments (FVST) is amenable to the novel iterative compression technique, and we provide a depth-bounded search tree for Feedback Arc Set in bipartite tournaments  ...  Following the same approach, we derive a fixed-parameter algorithm for Feedback Arc Set in bipartite tournaments (FASBT).  ... 
doi:10.1007/11758471_31 fatcat:3uppqoabzjc37oyqe7tgl6rjre

Techniques for Practical Fixed-Parameter Algorithms

F. Huffner, R. Niedermeier, S. Wernicke
2007 Computer journal  
The fixed-parameter approach is an algorithm design technique for solving combinatorially hard (mostly NP-hard) problems.  ...  For some of these problems, it can lead to algorithms that are both efficient and yet at the same time guaranteed to find optimal solutions.  ...  [66] to develop a (non-parameterized) faster algorithm for this problem.  ... 
doi:10.1093/comjnl/bxm040 fatcat:jbffitiefzfexftg3lgl7xnsza

On tractable cases of Target Set Selection

André Nichterlein, Rolf Niedermeier, Johannes Uhlmann, Mathias Weller
2012 Social Network Analysis and Mining  
TSS can be efficiently solved on graphs with small feedback edge set number and also turns out to be fixed-parameter tractable when parameterized by the vertex cover number, both results contrasting known  ...  While these tractability results are relevant for sparse networks, we also show efficient fixed-parameter algorithms for the parameter cluster edge deletion number, yielding tractability for certain dense  ...  Like the vertex cover number τ , the feedback edge set number f is a "weaker" parameter than treewidth, raising hope for faster algorithms for TSS in cases where f is small.  ... 
doi:10.1007/s13278-012-0067-7 fatcat:k2q4nk4qnbatnemcvpvm32tqjq

On Tractable Cases of Target Set Selection [chapter]

André Nichterlein, Rolf Niedermeier, Johannes Uhlmann, Mathias Weller
2010 Lecture Notes in Computer Science  
TSS can be efficiently solved on graphs with small feedback edge set number and also turns out to be fixed-parameter tractable when parameterized by the vertex cover number, both results contrasting known  ...  While these tractability results are relevant for sparse networks, we also show efficient fixed-parameter algorithms for the parameter cluster edge deletion number, yielding tractability for certain dense  ...  Like the vertex cover number τ , the feedback edge set number f is a "weaker" parameter than treewidth, raising hope for faster algorithms for TSS in cases where f is small.  ... 
doi:10.1007/978-3-642-17517-6_34 fatcat:utuzuybyojah5iljtjbk3j2cuq

Some Parameterized Problems On Digraphs

G. Gutin, A. Yeo
2007 Computer journal  
The problems include the feedback vertex and arc set problems, induced subdigraph problems and directed k-leaf problems. We also prove some new results on the topic.  ...  We survey results and open questions on complexity of parameterized problems on digraphs.  ...  Acknowledgements We are thankful to the referee for several important suggestions and for proving us with [48] . Research of both authors was supported in part by an EPSRC grant.  ... 
doi:10.1093/comjnl/bxm039 fatcat:5yqonwpu2jgqfkuv7itpc7j3km

Extended MSO Model Checking via Small Vertex Integrity [article]

Tatsuya Gima, Yota Otachi
2022 arXiv   pre-print
We show that the problem is fixed-parameter tractable parameterized by vertex integrity, where vertex integrity is a graph parameter standing between vertex cover number and treedepth.  ...  Our result thus narrows the gap between the fixed-parameter tractability parameterized by vertex cover number and the W[1]-hardness parameterized by treedepth.  ...  Acknowledgements The authors thank Michael Lampis and Valia Mitsou for fruitful discussions and sharing a preliminary version of [45] .  ... 
arXiv:2202.08445v3 fatcat:whndbaukenasjjdprpfqlwsc5q

A fixed-parameter algorithm for the directed feedback vertex set problem

Jianer Chen, Yang Liu, Songjian Lu, Barry O'sullivan, Igor Razgon
2008 Journal of the ACM  
The (parameterized) feedback vertex set problem on directed graphs, which we refer to as the dfvs problem, is defined as follows: given a directed graph G and a parameter k, either construct a feedback  ...  In this paper we develop new algorithmic techniques that result in an algorithm with running time 4 k k!n O(1) for the dfvs problem, thus showing that this problem is fixed-parameter tractable.  ...  In the last three years, the use of iterative compression facilitated the resolution of the status of fixed parameter tractability, and the design of faster parameterized algorithms, for a number of problems  ... 
doi:10.1145/1411509.1411511 fatcat:lxicbc7f3bgldllq7ubcjuui6y

A fixed-parameter algorithm for the directed feedback vertex set problem

Jianer Chen, Yang Liu, Songjian Lu, Barry O'Sullivan, Igor Razgon
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
The (parameterized) feedback vertex set problem on directed graphs, which we refer to as the dfvs problem, is defined as follows: given a directed graph G and a parameter k, either construct a feedback  ...  In this paper we develop new algorithmic techniques that result in an algorithm with running time 4 k k!n O(1) for the dfvs problem, thus showing that this problem is fixed-parameter tractable.  ...  In the last three years, the use of iterative compression facilitated the resolution of the status of fixed parameter tractability, and the design of faster parameterized algorithms, for a number of problems  ... 
doi:10.1145/1374376.1374404 dblp:conf/stoc/ChenLL08 fatcat:akj3qzdb75apjc3n3uk7ixu5au
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