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Fundamentals Of Parameterized Complexity
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Book Synopsis Parameterized Complexity by : Rodney G. Downey
Download or read book Parameterized Complexity written by Rodney G. Downey and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fundamentals of Parameterized Complexity by : Rodney G. Downey
Download or read book Fundamentals of Parameterized Complexity written by Rodney G. Downey and published by Springer Science & Business Media. This book was released on 2013-12-03 with total page 765 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years.
Book Synopsis Parameterized Complexity Theory by : J. Flum
Download or read book Parameterized Complexity Theory written by J. Flum and published by Springer Science & Business Media. This book was released on 2006-05-01 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a state-of-the-art introduction into both algorithmic techniques for fixed-parameter tractability and the structural theory of parameterized complexity classes. It presents detailed proofs of recent advanced results that have not appeared in book form before and replaces the earlier publication "Parameterized Complexity" by Downey and Fellows as the definitive book on this subject. The book will interest computer scientists, mathematicians and graduate students engaged with algorithms and problem complexity.
Book Synopsis Parameterized and Exact Computation by : Dániel Marx
Download or read book Parameterized and Exact Computation written by Dániel Marx and published by Springer Science & Business Media. This book was released on 2012-03-16 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Symposium on Parameterized and Exact Computation, IPEC 2011, in Saarbrücken, Germany, in September 2011. The 21 revised full papers presented were carefully reviewed and selected from 40 submissions. The topics addressed cover research in all aspects of parameterized and exact computation and complexity, including but not limited to new techniques for the design and analysis of parameterized and exact algorithms, fixed-parameter tractability results, parameterized complexity theory, relationship between parameterized complexity and traditional complexity classifications, applications of parameterized and exact computation, and implementation issues of parameterized and exact algorithms.
Book Synopsis Parameterized Complexity in the Polynomial Hierarchy by : Ronald de Haan
Download or read book Parameterized Complexity in the Polynomial Hierarchy written by Ronald de Haan and published by Springer Nature. This book was released on 2019-12-30 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parameterized Complexity in the Polynomial Hierarchy was co-recipient of the E.W. Beth Dissertation Prize 2017 for outstanding dissertations in the fields of logic, language, and information. This work extends the theory of parameterized complexity to higher levels of the Polynomial Hierarchy (PH). For problems at higher levels of the PH, a promising solving approach is to develop fixed-parameter tractable reductions to SAT, and to subsequently use a SAT solving algorithm to solve the problem. In this dissertation, a theoretical toolbox is developed that can be used to classify in which cases this is possible. The use of this toolbox is illustrated by applying it to analyze a wide range of problems from various areas of computer science and artificial intelligence.
Book Synopsis Computability and Complexity by : Rod G. Downey
Download or read book Computability and Complexity written by Rod G. Downey and published by Springer Nature. This book was released on 2024 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ideas and techniques comprised in the mathematical framework for understanding computation should form part of the standard background of a graduate in mathematics or computer science, as the issues of computability and complexity permeate modern science. This textbook/reference offers a straightforward and thorough grounding in the theory of computability and computational complexity. Among topics covered are basic naive set theory, regular languages and automata, models of computation, partial recursive functions, undecidability proofs, classical computability theory including the arithmetical hierarchy and the priority method, the basics of computational complexity and hierarchy theorems. Topics and features: · Explores Conway's undecidability proof of the "3x+1" problem using reductions from Register Machines and "Fractran" · Offers an accessible account of the undecidability of the exponential version of Hilbert's 10th problem due to Jones and Matijacevič · Provides basic material on computable structure, such as computable linear orderings · Addresses parameterized complexity theory, including applications to algorithmic lower bounds and kernelization lower bounds · Delivers a short account of generic-case complexity and of smoothed analysis · Includes bonus material on structural complexity theory and priority arguments in computability theory This comprehensive textbook will be ideal for advanced undergraduates or beginning graduates, preparing them well for more advanced studies or applications in science. Additionally, it could serve such needs for mathematicians or for scientists working in computational areas, such as biology.
Book Synopsis Theory of Computational Complexity by : Ding-Zhu Du
Download or read book Theory of Computational Complexity written by Ding-Zhu Du and published by John Wiley & Sons. This book was released on 2014-07-18 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition "...complete, up-to-date coverage of computational complexitytheory...the book promises to become the standard reference oncomputational complexity." -Zentralblatt MATH A thorough revision based on advances in the field ofcomputational complexity and readers’ feedback, the SecondEdition of Theory of Computational Complexity presentsupdates to the principles and applications essential tounderstanding modern computational complexity theory. The newedition continues to serve as a comprehensive resource on the useof software and computational approaches for solving algorithmicproblems and the related difficulties that can be encountered. Maintaining extensive and detailed coverage, Theory ofComputational Complexity, Second Edition, examines the theoryand methods behind complexity theory, such as computational models,decision tree complexity, circuit complexity, and probabilisticcomplexity. The Second Edition also features recentdevelopments on areas such as NP-completeness theory, as wellas: A new combinatorial proof of the PCP theorem based on thenotion of expander graphs, a research area in the field of computerscience Additional exercises at varying levels of difficulty to furthertest comprehension of the presented material End-of-chapter literature reviews that summarize each topic andoffer additional sources for further study Theory of Computational Complexity, Second Edition, is anexcellent textbook for courses on computational theory andcomplexity at the graduate level. The book is also a usefulreference for practitioners in the fields of computer science,engineering, and mathematics who utilize state-of-the-art softwareand computational methods to conduct research. Athorough revision based on advances in the field of computationalcomplexity and readers’feedback,the Second Edition of Theory of Computational Complexity presentsupdates to theprinciplesand applications essential to understanding modern computationalcomplexitytheory.The new edition continues to serve as a comprehensive resource onthe use of softwareandcomputational approaches for solving algorithmic problems and therelated difficulties thatcanbe encountered.Maintainingextensive and detailed coverage, Theory of ComputationalComplexity, SecondEdition,examines the theory and methods behind complexity theory, such ascomputationalmodels,decision tree complexity, circuit complexity, and probabilisticcomplexity. The SecondEditionalso features recent developments on areas such as NP-completenesstheory, as well as:•A new combinatorial proof of the PCP theorem based on the notion ofexpandergraphs,a research area in the field of computer science•Additional exercises at varying levels of difficulty to furthertest comprehension ofthepresented material•End-of-chapter literature reviews that summarize each topic andoffer additionalsourcesfor further studyTheoryof Computational Complexity, Second Edition, is an excellenttextbook for courses oncomputationaltheory and complexity at the graduate level. The book is also auseful referenceforpractitioners in the fields of computer science, engineering, andmathematics who utilizestate-of-the-artsoftware and computational methods to conduct research.
Book Synopsis Parameterized Complexity by : Rod Downey
Download or read book Parameterized Complexity written by Rod Downey and published by . This book was released on 1998 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parameterized Complexity After (almost) 10 Years by : Rod Downey
Download or read book Parameterized Complexity After (almost) 10 Years written by Rod Downey and published by . This book was released on 1998 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Frontiers in Parameterized Complexity and Algorithms by : Frances Rosamond
Download or read book New Frontiers in Parameterized Complexity and Algorithms written by Frances Rosamond and published by . This book was released on 2024-06-13 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research on parameterized complexity (PC), described in these peer-reviewed chapters by esteemed researchers, provides ties to practice as well as new theoretical developments, many in the direction of AI. Applications in bioinformatics and social choice are described, as well as faster, less costly approximation methods and new techniques using machine learning to find treewidth and other metrics. Many practical problems can be solved by harnessing the power of both PC and SAT solvers or integer linear programming modeled by parameterized graph problems. The extremely rapid development and deployment of PC continues to bring fresh understanding and solutions to fundamental open questions.
Book Synopsis Introduction to the Theory of Complexity by : Daniel Pierre Bovet
Download or read book Introduction to the Theory of Complexity written by Daniel Pierre Bovet and published by Prentice Hall PTR. This book was released on 1994 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a balanced approach that is partly algorithmic and partly structuralist, this book systematically reviews the most significant results obtained in the study of computational complexity theory. Features over 120 worked examples, over 200 problems, and 400 figures.
Book Synopsis Computability and Complexity by : Rod Downey
Download or read book Computability and Complexity written by Rod Downey and published by Springer. This book was released on 2024-05-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about computation, something which is ubiquitous in the modern world. More precisely, it examines computability theory and computational complexity theory. Computability theory is the part of mathematics and computer science which seeks to clarify what we mean by computation or algorithm. When is there a computational solution possible to some question? How can we show that none is possible? How computationally hard is the question we are concerned with? Arguably, this area lead to the development of digital computers. (Computational) complexity theory is an intellectual heir of computability theory. Complexity theory is concerned with understanding what resources are needed for computation, where typically we would measure the resources in terms of time and space. Can we perform some task in a feasible number of steps? Can we perform some algorithm with only a limited memory? Does randomness help? Are there standard approaches to overcoming computational difficulty?
Book Synopsis Characterizing Hardness in Parameterized Complexity by : Tarique Islam
Download or read book Characterizing Hardness in Parameterized Complexity written by Tarique Islam and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Parameterized complexity theory relaxes the classical notion of tractability and allows to solve some classically hard problems in a reasonably efficient way. However, many problems of interest remain intractable in the context of parameterized complexity. A completeness theory to categorize such problems has been developed based on problems on circuits and Model Checking problems. Although a basic machine characterization was proposed, it was not explored any further. We develop a computational view of parameterized complexity theory based on resource-bounded programs that run on alternating random access machines. We develop both natural and normalized machine characterizations for the W[t] and L[t] classes. Based on the new characterizations, we derive the basic completeness results in parameterized complexity theory, from a computational perspective. Unlike the previous cases, our proofs follow the classical approach for showing basic NP-completeness results (Cook's Theorem, in particular). We give new proofs of the Normalization Theorem by showing that (i) the computation of a resource-bounded program on an alternating RAM can be represented by instances of corre- sponding basic parametric problems, and (ii) the basic parametric problems can be decided by programs respecting the corresponding resource bounds. Many of the fundamental results follow as a consequence of our new proof of the Normalization Theorem. Based on a natural characterization of the W[t] classes, we develop new structural results establishing relationships among the classes in the W-hierarchy, and the W[t] and L[t] classes. Nontrivial upper-bound beyond the second level of the W-hierarchy is quite uncommon. We make use of the ability to implement natural algorithms to show new upper bounds for several parametric problems. We show that Subset Sum, Maximal Irredundant Set, and Reachability Distance in Vector Addition Systems (Petri Nets) are in W[3], W[4], and W[5], respectively. In some cases, the new bounds result in new completeness results. We derive new lower bounds based on the normalized programs for the W[t] and L[t] classes. We show that Longest Common Subsequence, with parameter the number of strings, is hard for L[t], t >= 1, and for W[SAT]. We also show that Precedence Constrained Multiprocessor Scheduling, with parameter the number of processors, is hard for L[t], t >= 1.
Book Synopsis Fundamentals of Computation Theory by : Olaf Owe
Download or read book Fundamentals of Computation Theory written by Olaf Owe and published by Springer Science & Business Media. This book was released on 2011-08-09 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 18th International Symposium Fundamentals of Computation Theory, FCT 2011, held in Oslo, Norway, in August 2011. The 28 revised full papers presented were carefully reviewed and selected from 78 submissions. FCT 2011 focused on algorithms, formal methods, and emerging fields, such as ad hoc, dynamic and evolving systems; algorithmic game theory; computational biology; foundations of cloud computing and ubiquitous systems; and quantum computation.
Book Synopsis Parameterized Algorithms by : Marek Cygan
Download or read book Parameterized Algorithms written by Marek Cygan and published by Springer. This book was released on 2015-07-20 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.
Book Synopsis Fundamentals of Computation Theory by : Olaf Owe
Download or read book Fundamentals of Computation Theory written by Olaf Owe and published by Springer. This book was released on 2011-08-18 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 18th International Symposium Fundamentals of Computation Theory, FCT 2011, held in Oslo, Norway, in August 2011. The 28 revised full papers presented were carefully reviewed and selected from 78 submissions. FCT 2011 focused on algorithms, formal methods, and emerging fields, such as ad hoc, dynamic and evolving systems; algorithmic game theory; computational biology; foundations of cloud computing and ubiquitous systems; and quantum computation.
Book Synopsis Mathematical Foundations of Computer Science 2015 by : Giuseppe F. Italiano
Download or read book Mathematical Foundations of Computer Science 2015 written by Giuseppe F. Italiano and published by Springer. This book was released on 2015-08-10 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set LNCS 9234 and 9235 constitutes the refereed conference proceedings of the 40th International Symposium on Mathematical Foundations of Computer Science, MFCS 2015, held in Milan, Italy, in August 2015. The 82 revised full papers presented together with 5 invited talks were carefully selected from 201 submissions. The papers feature high-quality research in all branches of theoretical computer science. They have been organized in the following topical main sections: logic, semantics, automata, and theory of programming (volume 1) and algorithms, complexity, and games (volume 2).
