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On the existence of subexponential parameterized algorithms

Liming Cai, David Juedes
2003 Journal of computer and system sciences (Print)  
of Oð2 oð ffiffi k p Þ pðnÞÞ-time parameterized algorithms for a number of other important problems such as Dominating Set, Vertex Cover, and Independent Set on planar graph instances. r  ...  The existence of subexponential-time parameterized algorithms is examined for various parameterized problems solvable in time Oð2 OðkÞ pðnÞÞ: It is shown that for each tX1; there are parameterized problems  ...  at Schloss Dagstuhl for their valuable comments on a preliminary version of this work [12] .  ... 
doi:10.1016/s0022-0000(03)00074-6 fatcat:m7u6kffamfditepzv3ktkhwhry

On Parameterized Exponential Time Complexity [chapter]

Jianer Chen, Iyad A. Kanj, Ge Xia
2009 Lecture Notes in Computer Science  
For example, we show that the Planar Dominating Set problem on degree-3 graphs can be solved in 2 o( √ k) p(n) parameterized time if and only if the general Planar Dominating Set problem can.  ...  We show that a parameterized problem can be solved in parameterized 2 o(f (k)) p(n) time if and only if it is solvable in time O(2 δf (k) q(n)) for any constant δ > 0, where p and q are polynomials.  ...  [1] gave parameterized subexponential time algorithms for the Planar Vertex Cover, Planar Independent Set, and Planar Dominating Set problems that run in time 2 O( √ k) n.  ... 
doi:10.1007/978-3-642-02017-9_20 fatcat:tewlldzmfjalvpgbpazjvzg5ve

On parameterized exponential time complexity

Jianer Chen, Iyad A. Kanj, Ge Xia
2009 Theoretical Computer Science  
For example, we show that the Planar Dominating Set problem on degree-3 graphs can be solved in 2 o( √ k) p(n) parameterized time if and only if the general Planar Dominating Set problem can.  ...  We show that a parameterized problem can be solved in parameterized 2 o(f (k)) p(n) time if and only if it is solvable in time O(2 δf (k) q(n)) for any constant δ > 0, where p and q are polynomials.  ...  [1] gave parameterized subexponential time algorithms for the Planar Vertex Cover, Planar Independent Set, and Planar Dominating Set problems that run in time 2 O( √ k) n.  ... 
doi:10.1016/j.tcs.2009.03.006 fatcat:i2qixnqsvjaoveyv7b2wmotsnq

Parameterized algorithms of fundamental NP-hard problems: a survey

Wenjun Li, Yang Ding, Yongjie Yang, R. Simon Sherratt, Jong Hyuk Park, Jin Wang
2020 Human-Centric Computing and Information Sciences  
We give an overview on parameterized algorithms for some fundamental NP-hard problems, including MaxSAT, Maximum Internal Spanning Trees, Maximum Internal Out-Branching, Planar (Connected) Dominating Set  ...  Parameterized computation theory has developed rapidly over the last two decades.  ...  Acknowledgements The authors would like to thank the reviewers for their valuable comments which improve the quality of this paper dramatically.  ... 
doi:10.1186/s13673-020-00226-w fatcat:2ncywbdlnrdtzliiz4tyi76df4

Fast Sub-exponential Algorithms and Compactness in Planar Graphs [chapter]

Dimitrios M. Thilikos
2011 Lecture Notes in Computer Science  
Our framework is general enough to unify the analysis of almost all known sub-exponential parameterized algorithms on planar graphs and improves or matches their running times.  ...  Roughly speaking, a parameterized problem is (r, q)-compact when all the faces and vertices of its YESinstances are "r-radially dominated" by some vertex set whose size is at most q times the parameter  ...  The first sub-exponential parameterized algorithm on planar graphs appeared in [1] for Dominating Set, Independent Dominating Set, and Face Cover.  ... 
doi:10.1007/978-3-642-23719-5_31 fatcat:cp27q3vsafa3jdocezkmvdxgc4

Subexponential algorithms for partial cover problems

Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, Saket Saurabh
2011 Information Processing Letters  
[FSTTCS 08 ] whether there is a subexponential algorithm for Partial Vertex Cover and Partial Dominating Set.  ...  In general graphs, these problems are hard for parameterized complexity classes when parameterized by k. It was recently shown by Amini et. al.  ...  The algorithm for PVC was recently improved by Kneis et al. [23] .  ... 
doi:10.1016/j.ipl.2011.05.016 fatcat:y5evjiuiure35h36ulzmcfunsm

Fast Parameterized Algorithms for Graphs on Surfaces: Linear Kernel and Exponential Speed-Up [chapter]

Fedor V. Fomin, Dimitrios M. Thilikos
2004 Lecture Notes in Computer Science  
(ii) Using such a kernel we improve the best so far algorithm for k-dominating set on graphs of genus (iii) Applying tools from the topological graph theory, we improve drastically the best so far combinatorial  ...  Our new bound provides further exponential speed-up of our algorithm for the k-dominating set and we prove that the same speed-up applies for a wide category of parameterized graph problems such as k-vertex  ...  The first fixed-parameter algorithm for k-dominating set in planar graphs [9] has running time O(11 k n); subsequently, the first subexponential parameterized algorithm with running time O(4 6 √ 34k  ... 
doi:10.1007/978-3-540-27836-8_50 fatcat:l66jjmhyyff4rjblksq5ea4xgy

Subexponential Parameterized Algorithms [chapter]

FedorV. Fomin
2015 Encyclopedia of Algorithms  
We give a review of a series of techniques and results on the design of subexponential parameterized algorithms for graph problems.  ...  As a result, we have 2 O( √ k) · n O(1) time algorithms for a wide variety of parameterized problems on graphs, where n is the size of the graph and k is the parameter.  ...  We take the opportunity to warmly thank Hans Bodlaender, Erik Demaine, MohammadTaghi Hajiaghayi, Naomi Nishimura and Eelko Penninkx and Prabhakar Ragde for collaborating with us on this project.  ... 
doi:10.1007/978-3-642-27848-8_780-2 fatcat:6qnit73yivamjaqhs5eubsnekm

Subexponential Parameterized Algorithms [chapter]

Fedor V. Fomin
2015 Encyclopedia of Algorithms  
We give a review of a series of techniques and results on the design of subexponential parameterized algorithms for graph problems.  ...  As a result, we have 2 O( √ k) · n O(1) time algorithms for a wide variety of parameterized problems on graphs, where n is the size of the graph and k is the parameter.  ...  We take the opportunity to warmly thank Hans Bodlaender, Erik Demaine, MohammadTaghi Hajiaghayi, Naomi Nishimura and Eelko Penninkx and Prabhakar Ragde for collaborating with us on this project.  ... 
doi:10.1007/978-3-642-27848-8_780-1 fatcat:rsubc5ln7zdrvb3kt5eir2xcsy

Subexponential Parameterized Algorithms [chapter]

Fedor V. Fomin
2016 Encyclopedia of Algorithms  
We give a review of a series of techniques and results on the design of subexponential parameterized algorithms for graph problems.  ...  As a result, we have 2 O( √ k) · n O(1) time algorithms for a wide variety of parameterized problems on graphs, where n is the size of the graph and k is the parameter.  ...  We take the opportunity to warmly thank Hans Bodlaender, Erik Demaine, MohammadTaghi Hajiaghayi, Naomi Nishimura and Eelko Penninkx and Prabhakar Ragde for collaborating with us on this project.  ... 
doi:10.1007/978-1-4939-2864-4_780 fatcat:swjyxbzjejebxbxynfoun7vqem

Safe Approximation and Its Relation to Kernelization [chapter]

Jiong Guo, Iyad Kanj, Stefan Kratsch
2012 Lecture Notes in Computer Science  
We demonstrate how the notion of safe approximation can be useful in designing kernelization algorithms for certain fixed-parameter tractable problems.  ...  We introduce a notion of approximation, called safe approximation, for minimization problems that are subset problems.  ...  The authors would like to thank Bart Jansen for suggesting the nice example used in the proof of Theorem 4.  ... 
doi:10.1007/978-3-642-28050-4_14 fatcat:2c7xqcqavrh7jae74ms2ndbowe

Subexponential parameterized algorithms

Frederic Dorn, Fedor V. Fomin, Dimitrios M. Thilikos
2008 Computer Science Review  
We give a review of a series of techniques and results on the design of subexponential parameterized algorithms for graph problems.  ...  As a result, we have 2 O( √ k) · n O(1) time algorithms for a wide variety of parameterized problems on graphs, where n is the size of the graph and k is the parameter.  ...  We take the opportunity to warmly thank Hans Bodlaender, Erik Demaine, MohammadTaghi Hajiaghayi, Naomi Nishimura and Eelko Penninkx and Prabhakar Ragde for collaborating with us on this project.  ... 
doi:10.1016/j.cosrev.2008.02.004 fatcat:s3v36rxv6zeqjosops4lrsueay

What's Next? Future Directions in Parameterized Complexity [chapter]

Dániel Marx
2012 Lecture Notes in Computer Science  
In particular, we set up a framework for understanding which problems can be solved by branching algorithms.  ...  First, we point out that the search for optimality in parameterized complexity already has good foundations, but lots of interesting work can be still done in this area.  ...  Assuming ETH, there is no 2 o( √ k) · n O(1) time algorithm for Independent Set, Dominating Set, and k-Path on planar graphs, where k is the size of the solution to be found.  ... 
doi:10.1007/978-3-642-30891-8_20 fatcat:enftdcd27rd5jmglgw4khqffty

nonblocker: Parameterized Algorithmics for minimum dominating set [chapter]

Frank Dehne, Michael Fellows, Henning Fernau, Elena Prieto, Frances Rosamond
2006 Lecture Notes in Computer Science  
We provide parameterized algorithms for nonblocker, the parametric dual of the well known dominating set problem.  ...  in order to obtain very small kernels, (ii) use of known exact algorithms for the (nonparameterized) minimum dominating set problem, and (iii) use of exponential space.  ...  We have presented two efficient parameterized algorithms for the nonblocker problem, the parametric dual of dominating set.  ... 
doi:10.1007/11611257_21 fatcat:qnoolxub6rhixpf3an5vavlv74

Ubiquitous Parameterization — Invitation to Fixed-Parameter Algorithms [chapter]

Rolf Niedermeier
2004 Lecture Notes in Computer Science  
Hence, the study of parameterized complexity for computationally hard problems is proving highly fruitful.  ...  The purpose of this article is to stir the reader's interest in this field by providing a gentle introduction to the rewarding field of fixed-parameter algorithms.  ...  I am very grateful to Rod Downey, Michael Fellows, Jens Gramm, Jiong Guo, Falk Hüffner, Klaus-Jörn Lange, Catherine McCartin, Naomi Nishimura, and Prabhakar Ragde for their constructive feedback on a preliminary  ... 
doi:10.1007/978-3-540-28629-5_4 fatcat:vf5gtr3u7jceblnz2ucj77hmky
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