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On the parameterized complexity of approximate counting

J. Andrés Montoya
2011 RAIRO - Theoretical Informatics and Applications  
In this paper we study the parameterized complexity of approximating the parameterized counting problems contained in the class #W [P ] ; the parameterized analogue of #P: We prove a parameterized analogue  ...  of a famous theorem of Stockmeyer claiming that approximate counting belongs to the second level of the polynomial hierarchy.  ...  The author especially thanks the anonymous referee for carefully reading the manuscript and for providing him with many helpful suggestions which have greatly improved his writing.  ... 
doi:10.1051/ita/2011007 fatcat:6ap2lmniqnfx7f6mlbuzaak2ea

Counting problems in parameterized complexity

Chihao Zhang, Yijia Chen
2014 Tsinghua Science and Technology  
It leads to practically efficient algorithms for many NP-hard problems and also provides a much finer complexity classification for other intractable problems.  ...  Although the theory is mostly on decision problems, parameterized complexity naturally extends to counting problems as well.  ...  ., Courcelle's Theorem and the framework of Holant problems. We also discussed some randomized approximation counting algorithms.  ... 
doi:10.1109/tst.2014.6867521 fatcat:tluyfiannbgt3fmduir4ctsfje

Counting Problems in Parameterized Complexity

Radu Curticapean, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
This survey is an invitation to parameterized counting problems for readers with a background in parameterized algorithms and complexity.  ...  ACM Subject Classification Theory of computation → Parameterized complexity and exact algorithms, Theory of computation → Problems, reductions and completeness Keywords and phrases counting complexity,  ...  Techniques for counting problems To gain some intuition for the algorithmic boundary of parameterized counting, let us examine the fates of some techniques for parameterized algorithms as we go from decision  ... 
doi:10.4230/lipics.ipec.2018.1 dblp:conf/iwpec/Curticapean18 fatcat:tdfs7zngzrgv5fixf2qawrccuy

Data-Compression for Parametrized Counting Problems on Sparse Graphs

Eun Jung Kim, Maria Serna, Dimitrios M. Thilikos, Michael Wagner
2018 International Symposium on Algorithms and Computation  
We study a family of vertex-certified counting problems on graphs that are MSOL-expressible; that is, for an MSOL-formula φ with one free set variable to be interpreted as a vertex subset, we want to count  ...  We study the concept of compactor, which may be seen as a counting-analogue of kernelization in counting parameterized complexity.  ...  In some cases, such theorems have a counterpart on counting parameterized problems.  ... 
doi:10.4230/lipics.isaac.2018.20 dblp:conf/isaac/0002ST18 fatcat:xytw4ioxsbelxko3iv4tmutely

Parameterized Complexity and Approximation Algorithms

D. Marx
2007 Computer journal  
Approximation algorithms and parameterized complexity are usually considered to be two separate ways of dealing with hard algorithmic problems.  ...  We discuss the different ways parameterized complexity can be extended to approximation algorithms, survey results of this type, and propose directions for future research.  ...  ACKNOWLEDGMENTS I would like to thank Mike Fellows for asking me to write this survey, and for the many ideas, comments, and references that were essential in compiling the material.  ... 
doi:10.1093/comjnl/bxm048 fatcat:6yukdt7tvja3jf76zyuxfm536q

Special Issue "New Frontiers in Parameterized Complexity and Algorithms": Foreward by the Guest Editors

Neeldhara Misra, Frances Rosamond, Meirav Zehavi
2020 Algorithms  
This Special Issue contains eleven articles—surveys and research papers—that represent fresh and ambitious new directions in the area of Parameterized Complexity.  ...  Approximation algorithms, like Parameterized Complexity, is a framework to deal with computationally hard problems.  ...  For example, we can achieve a (1 + )-approximate solution in FPT time for a problem that is unlikely to admit any constant-factor approximation algorithm in polynomial time and which is W[1]-hard, and  ... 
doi:10.3390/a13090236 fatcat:ptrl6x2yjzd57h7ctdgsfklsiq

Parameterized Exact and Approximation Algorithms for Maximum k-Set Cover and Related Satisfiability Problems [article]

Edouard Bonnet, Vangelis Th. Paschos, Florian Sikora
2016 arXiv   pre-print
This problem is W[2]-hard when parameterized by k, and FPT when parameterized by p. We investigate the parameterized approximability of the problem with respect to parameters k and p.  ...  Then, we show that Max Sat-k, a satisfiability problem generalizing Max k-Set Cover, is also FPT with respect to parameter p.  ...  For item 2, we will show how parameterized (with respect to k) approximability of max k-set cover within ratio 1− c /n, for some constant c > 1, would lead to parameterized approximability of min dominating  ... 
arXiv:1309.4718v3 fatcat:gvl4qbeizjamvgjb6imcfigfgu

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 15301)

Andrei A. Bulatov, Venkatesan Guruswami, Andrei Krokhin, Dániel Marx, Marc Herbstritt
2016 Dagstuhl Reports  
tasks related to the constraint satisfaction problem (CSP), as well as the applicability/limitations of algorithmic techniques.  ...  The Dagstuhl Seminar 15301 "The Constraint Satisfaction Problem: Complexity and Approximability" was aimed at bringing together researchers using all the different techniques in the study of the CSP, so  ...  The latter problem, called #BIS, is a complete problem in an important complexity class for approximate counting, and is believed not to have an efficient approximation algorithm or FPRAS.  ... 
doi:10.4230/dagrep.5.7.22 dblp:journals/dagstuhl-reports/BulatovGKM15 fatcat:lcyvfsxsbzbrfe27irlpxepxoi

Randomization in Parameterized Complexity (Dagstuhl Seminar 17041)

Marek Cygan, Fedor V. Fomin, Danny Hermelin, Magnus Wahlström, Marc Herbstritt
2017 Dagstuhl Reports  
Dagstuhl Seminar 17041 "Randomization in Parameterized Complexity" took place from January 22nd to January 27th 2017 with the objective to bridge the gap between randomization and parameterized complexity  ...  We note that extending our algorithmic findings to binary matroids, a superclass of regular matroids, is highly unlikely: Minimum Spanning Circuit parameterized by is W [1] -hard on binary matroids even  ...  More precisely, we prove that Minimum Spanning Circuit parameterized by |T | is W [1] -hard even on cographic matroids, a proper subclass of regular matroids.  ... 
doi:10.4230/dagrep.7.1.103 dblp:journals/dagstuhl-reports/CyganFHW17 fatcat:vjbkuavqdzew3nbk6wjvmpbd5m

Parameterized approximation of dominating set problems

Rodney G. Downey, Michael R. Fellows, Catherine McCartin, Frances Rosamond
2008 Information Processing Letters  
We answer the analogous problem completely for the related Independent Dominating Set (IDS) problem, showing that IDS does not admit an FPT approximation algorithm, for any g(k), unless F P T = W [2].  ...  Such an outcome is termed an FPT approximation algorithm. We describe some results that begin to provide some answers.  ...  Introduction Most of the work in the area of parameterized complexity and algorithmics to date has focused on exact algorithms for decision problems.  ... 
doi:10.1016/j.ipl.2008.09.017 fatcat:zi6b7dfoujdvng5gpiprxjkryu

On Parameterized Intractability: Hardness and Completeness

J. Chen, J. Meng
2007 Computer journal  
natural computational problems.  ...  We study the theory and techniques developed in the research of parameterized intractability, emphasizing on parameterized hardness and completeness that imply (stronger) computational lower bounds for  ...  Analogically, we can consider parameterized counting complexity for various problems.  ... 
doi:10.1093/comjnl/bxm036 fatcat:wjrw57b5nvbfnfib3uii5tviiq

Optimality and tight results in parameterized complexity (Dagstuhl Seminar 14451)

Stefan Kratsch, Daniel Lokshtanov, Dániel Marx, Peter Rossmanith, Marc Herbstritt
2015 Dagstuhl Reports  
Over the last two decades parameterized complexity has become one of the main tools for handling intractable problems.  ...  Recently, tools have been developed not only to classify problems, but also to make statements about how close an algorithm is to being optimal with respect to running time.  ...  Some examples of results that would refute SETH include: a truly subquadratic time 1.499-approximation algorithm for the diameter problem in sparse graphs, any fully dynamic algorithm for maintaining the  ... 
doi:10.4230/dagrep.4.11.1 dblp:journals/dagstuhl-reports/KratschLMR14 fatcat:vwgmhttkgrf4pb34jpsb2rfvnm

Parameterized exact and approximation algorithms for maximumk-set cover and related satisfiability problems

Édouard Bonnet, Vangelis Th. Paschos, Florian Sikora
2016 RAIRO - Theoretical Informatics and Applications  
This problem is W[2]-hard when parameterized by k, and FPT when parameterized by p. We investigate the parameterized approximability of the problem with respect to parameters k and p.  ...  Then, we show that max sat-k, a satisfiability problem generalizing max k-set cover, is also FPT with respect to parameter p.  ...  In fact, we are going to prove a stronger result, claiming that, for any polynomial approximation ratio r achieved by some polynomial time algorithm APPROX and any parameterized algorithm PARAM(π) for  ... 
doi:10.1051/ita/2016022 fatcat:urg3gnvtobbajnkjijvq57pmru

Data-compression for Parametrized Counting Problems on Sparse graphs [article]

Eun Jung Kim, Maria Serna, Dimitrios M. Thilikos
2018 arXiv   pre-print
We study a family of vertex-certified counting problems on graphs that are MSOL-expressible; that is, for an MSOL-formula ϕ with one free set variable to be interpreted as a vertex subset, we want to count  ...  We study the concept of compactor, which may be seen as a counting-analogue of kernelization in counting parameterized complexity.  ...  counting problems.  ... 
arXiv:1809.08160v2 fatcat:dwejq5ok25dv5hto3moiejvjva

Parameterized Counting Problems [chapter]

Catherine McCartin
2002 Lecture Notes in Computer Science  
However, it is becoming evident that the parameterized point o f view can lead to new insight i n to counting problems.  ...  The goal of this article is to introduce a formal framework in which o n e m a y consider parameterized counting problems.  ...  To consider`hard' parameterized counting problems, we need some more de nitions: De nition 8 (Parameterized transformation).  ... 
doi:10.1007/3-540-45687-2_46 fatcat:j72yfgceqnbhrajuomkuiroytm
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