Journal ArticleDOI
Parameterized Complexity and Approximation Algorithms
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The different ways parameterized complexity can be extended to approximation algorithms, survey results of this type and proposed directions for future research are discussed.Abstract:
Approximation algorithms and parameterized complexity are usually considered to be two separate ways of dealing with hard algorithmic problems. In this paper, our aim is to investigate how these two fields can be combined to achieve better algorithms than what any of the two theories could offer. We discuss the different ways parameterized complexity can be extended to approximation algorithms, survey results of this type and propose directions for future research.read more
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Book
Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
Journal ArticleDOI
Invitation to data reduction and problem kernelization
Jiong Guo,Rolf Niedermeier +1 more
TL;DR: A brief survey is presented that presents data reduction and problem kernelization as a promising research field for algorithm and complexity theory.
Journal ArticleDOI
Infeasibility of instance compression and succinct PCPs for NP
Lance Fortnow,Rahul Santhanam +1 more
TL;DR: There is no reduction from OR-SAT to any set A where the length of the output is bounded by a polynomial in n, unless NP@?coNP/poly, and the Polynomial-Time Hierarchy collapses.
Proceedings ArticleDOI
Infeasibility of instance compression and succinct PCPs for NP
Lance Fortnow,Rahul Santhanam +1 more
TL;DR: In this article, it was shown that there is no reduction from OR-SAT to any set A where the length of the output is bounded by a polynomial in n, unless NP ⊆ coNP/poly, and the Polynomial-Time Hierarchy collapses.
Book
Kernelization: Theory of Parameterized Preprocessing
TL;DR: Kernelization: Theory of Parameterized Preprocessing, by Fomin et al., is unique in that it is a text focusing solely on the titular topic of kernelization, and is able to more effectively showcase and teach the tools used in the field than a more traditional text on fixed parameter complexity.
References
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Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Graph Theory
TL;DR: Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results.
Book
Parameterized Complexity
TL;DR: An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability, and introduces readers to new classes of algorithms which may be analysed more precisely than was the case until now.
Journal ArticleDOI
The complexity of computing the permanent
TL;DR: It is shown that the permanent function of (0, 1)-matrices is a complete problem for the class of counting problems associated with nondeterministic polynomial time computations.