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About 4,195 papers for “Parameterized complexity”

Parameterized complexity

Gries, David, Schneider, Fred B, Downey, R G · CERN Document Server (European Organization for Nuclear Research) · 1999

Cited by 0

Parameterized Complexity

Ondřej Suchý · Digital Repository (National Repository of Grey Literature) · 2011

Title: Parameterized Complexity Author: Ondřej Suchý Department: Department of Applied Mathematics Advisor: Prof. RNDr. Jan Kratochvíl, CSc. Advisor's e-mail address: honza@kam.mff.cuni.cz Abstract: This thesis deals with the parameterized complexity of NP-hard graph problems. We explore the complexity of the problems in various scenarios, with respect to miscellaneous parameters and their combina- tions. Our aim is rather to classify in this multivariate manner whether the particular parameters make the problem fixed-parameter tractable or intractable than to present the algorithm achieving the best running time. In the questions we study typically the first-choice parameter is unsuccessful, in which case we propose to use less standard ones. The first family of problems investigated provides a common general- ization of many well known and studied domination and independence problems. Here we suggest using the dual parameterization and show that, in contrast to the standard solution-size, it can confine the in- evitable combinatorial explosion. Further studied problems are ana- logues of the Steiner problem in directed graphs. Here the parameter- ization by the number of terminals to be connected seems to be previ- ously unexplored in the directed setting. Unfortunately, the problems are shown to be...

Cited by 0

Parameterized Complexity

Michael R. Fellows · Electronic Notes in Theoretical Computer Science · 2002

An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability. The authors consider the problem in terms of parameterized languages and taking k-slices of the language, thus introducing readers to new classes of algorithms which may be analysed more precisely than was the case until now. The book is as self-contained as possible and includes a great deal of background material. As a result, computer scientists, mathematicians, and graduate students interested in the design and analysis of algorithms will find much of interest.

Cited by 2,884Open access

Parameterized Complexity

Rodney G. Downey, Michael R. Fellows · Texts and monographs in computer science · 1999

Cited by 2,510

Parameterized learning complexity

Rodney G. Downey, Patricia Evans, Michael R. Fellows · 1993

Article Free Access Share on Parameterized learning complexity Authors: Rodney G. Downey View Profile , Patricia A. Evans View Profile , Michael R. Fellows View Profile Authors Info & Claims COLT '93: Proceedings of the sixth annual conference on Computational learning theoryAugust 1993 Pages 51–57https://doi.org/10.1145/168304.168311Online:01 August 1993Publication History 20citation381DownloadsMetricsTotal Citations20Total Downloads381Last 12 Months10Last 6 weeks3 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Cited by 42Open access

Parameterized Complexity Classes

Iris van Rooij, Mark Blokpoel, Johan Kwisthout et al. · Cambridge University Press eBooks · 2019

In this chapter we introduce the parameterized analogues of \pt\ and \np, namely, \fpt and other complexity classes such as \wone, \wtwo, and \xp\ comprising with \fpt\ the \whi-hierarchy, and the formal notions of \whi-hardness and \whi-completeness. We describe why \whi-hard parameterized problems are considered to be fixed-parameter intractable (i.e., not computable in fixed-parameter tractable time). We explain how one can prove that a problem is a member of a class in the \whi-hierarchy, and how one can use the technique of parameterized reduction, introduced and practiced in Chapter 6, to prove \whi-hardness and \whi-completeness.

Cited by 0

Parameterized Proof Complexity

Stefan Dantchev, Barnaby Martin, Stefan Szeider · Durham Research Online (Durham University) · 2007

We propose a proof-theoretic approach for gaining evidence that certain parameterized problems are not fixed-parameter tractable. We consider proofs that witness that a given propositional CNF formula cannot be satisfied by a truth assignment that sets at most k variables to true, considering k as the parameter (we call such a formula a parameterized contradiction). One could separate the parameterized complexity classes FPT and W(M. Cesati, 2006) by showing that there is no fpt-bounded parameterized proof system, i.e., that there is no proof system that admits proofs of size f(k)n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(1)</sup> where f is a computable function and n represents the size of the propositional formula. By way of a first step, we introduce the system of parameterized tree-like resolution, and show that this system is not fpt-bounded. Indeed we give a general result on the size of shortest tree-like resolution proofs of parameterized contradictions that uniformly encode first-order principles over a universe of size n. We establish a dichotomy theorem that splits the exponential case of Riis's complexity-gap Theorem into two sub-cases, one that admits proofs of size f(k)n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(1)</sup> and one that does not. We also discuss how the set of parameterized contradictions may be embedded into the set of (ordinary) contradictions by the addition of new axioms. When embedded into general (DAG-like) resolution, we demonstrate that the pigeonhole principle has a proof of size 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This contrasts with the case of tree-like resolution where the embedded pigeonhole principle falls into the "non-FPT" category of our dichotomy.

Cited by 22Open access