Complexity Of Constraints
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Complexity Of Constraints
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Author : Nadia Creignou
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-18
Complexity Of Constraints written by Nadia Creignou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-18 with Computers categories.
Nowadays constraint satisfaction problems (CSPs) are ubiquitous in many different areas of computer science, from artificial intelligence and database systems to circuit design, network optimization, and theory of programming languages. Consequently, it is important to analyze and pinpoint the computational complexity of certain algorithmic tasks related to constraint satisfaction. The complexity-theoretic results of these tasks may have a direct impact on, for instance, the design and processing of database query languages, or strategies in data-mining, or the design and implementation of planners. This state-of-the-art survey contains the papers that were invited by the organizers after conclusion of an International Dagstuhl-Seminar on Complexity of Constraints, held in Dagstuhl Castle, Germany, in October 2006. A number of speakers were solicited to write surveys presenting the state of the art in their area of expertise. These contributions were peer-reviewed by experts in the field and revised before they were collated to the 9 papers of this volume. In addition, the volume contains a reprint of a survey by Kolaitis and Vardi on the logical approach to constraint satisfaction that first appeared in 'Finite Model Theory and its Applications', published by Springer in 2007.
Complexity Of Constraints
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Author : Nadia Creignou
language : en
Publisher:
Release Date : 2008
Complexity Of Constraints written by Nadia Creignou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Complexity Classifications Of Boolean Constraint Satisfaction Problems
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Author : Nadia Creignou
language : en
Publisher: SIAM
Release Date : 2001-01-01
Complexity Classifications Of Boolean Constraint Satisfaction Problems written by Nadia Creignou and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
Presents a novel form of a compendium that classifies an infinite number of problems by using a rule-based approach.
Applications Of Partial Polymorphisms In Fine Grained Complexity Of Constraint Satisfaction Problems
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Author : Biman Roy
language : en
Publisher: Linköping University Electronic Press
Release Date : 2020-03-23
Applications Of Partial Polymorphisms In Fine Grained Complexity Of Constraint Satisfaction Problems written by Biman Roy and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-23 with categories.
In this thesis we study the worst-case complexity ofconstraint satisfaction problems and some of its variants. We use methods from universal algebra: in particular, algebras of total functions and partial functions that are respectively known as clones and strong partial clones. The constraint satisfactionproblem parameterized by a set of relations ? (CSP(?)) is the following problem: given a set of variables restricted by a set of constraints based on the relations ?, is there an assignment to thevariables that satisfies all constraints? We refer to the set ? as aconstraint language. The inverse CSPproblem over ? (Inv-CSP(?)) asks the opposite: given a relation R, does there exist a CSP(?) instance with R as its set of models? When ? is a Boolean language, then we use the term SAT(?) instead of CSP(?) and Inv-SAT(?) instead of Inv-CSP(?). Fine-grained complexity is an approach in which we zoom inside a complexity class and classify theproblems in it based on their worst-case time complexities. We start by investigating the fine-grained complexity of NP-complete CSP(?) problems. An NP-complete CSP(?) problem is said to be easier than an NP-complete CSP(?) problem if the worst-case time complexity of CSP(?) is not higher thanthe worst-case time complexity of CSP(?). We first analyze the NP-complete SAT problems that are easier than monotone 1-in-3-SAT (which can be represented by SAT(R) for a certain relation R), and find out that there exists a continuum of such problems. For this, we use the connection between constraint languages and strong partial clones and exploit the fact that CSP(?) is easier than CSP(?) when the strong partial clone corresponding to ? contains the strong partial clone of ?. An NP-complete CSP(?) problem is said to be the easiest with respect to a variable domain D if it is easier than any other NP-complete CSP(?) problem of that domain. We show that for every finite domain there exists an easiest NP-complete problem for the ultraconservative CSP(?) problems. An ultraconservative CSP(?) is a special class of CSP problems where the constraint language containsall unary relations. We additionally show that no NP-complete CSP(?) problem can be solved insub-exponential time (i.e. in2^o(n) time where n is the number of variables) given that theexponentialtime hypothesisis true. Moving to classical complexity, we show that for any Boolean constraint language ?, Inv-SAT(?) is either in P or it is coNP-complete. This is a generalization of an earlier dichotomy result, which was only known to be true for ultraconservative constraint languages. We show that Inv-SAT(?) is coNP-complete if and only if the clone corresponding to ? contains essentially unary functions only. For arbitrary finite domains our results are not conclusive, but we manage to prove that theinversek-coloring problem is coNP-complete for each k>2. We exploit weak bases to prove many of theseresults. A weak base of a clone C is a constraint language that corresponds to the largest strong partia clone that contains C. It is known that for many decision problems X(?) that are parameterized bya constraint language ?(such as Inv-SAT), there are strong connections between the complexity of X(?) and weak bases. This fact can be exploited to achieve general complexity results. The Boolean domain is well-suited for this approach since we have a fairly good understanding of Boolean weak bases. In the final result of this thesis, we investigate the relationships between the weak bases in the Boolean domain based on their strong partial clones and completely classify them according to the setinclusion. To avoid a tedious case analysis, we introduce a technique that allows us to discard a largenumber of cases from further investigation.
Complexity Of Infinite Domain Constraint Satisfaction
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Author : Manuel Bodirsky
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-10
Complexity Of Infinite Domain Constraint Satisfaction written by Manuel Bodirsky and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-10 with Computers categories.
Introduces the universal-algebraic approach to classifying the computational complexity of constraint satisfaction problems.
Complexity In Numerical Optimization
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Author : Panos M. Pardalos
language : en
Publisher: World Scientific
Release Date : 1993
Complexity In Numerical Optimization written by Panos M. Pardalos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Computational complexity, originated from the interactions between computer science and numerical optimization, is one of the major theories that have revolutionized the approach to solving optimization problems and to analyzing their intrinsic difficulty.The main focus of complexity is the study of whether existing algorithms are efficient for the solution of problems, and which problems are likely to be tractable.The quest for developing efficient algorithms leads also to elegant general approaches for solving optimization problems, and reveals surprising connections among problems and their solutions.This book is a collection of articles on recent complexity developments in numerical optimization. The topics covered include complexity of approximation algorithms, new polynomial time algorithms for convex quadratic minimization, interior point algorithms, complexity issues regarding test generation of NP-hard problems, complexity of scheduling problems, min-max, fractional combinatorial optimization, fixed point computations and network flow problems.The collection of articles provide a broad spectrum of the direction in which research is going and help to elucidate the nature of computational complexity in optimization. The book will be a valuable source of information to faculty, students and researchers in numerical optimization and related areas.
The Complexity Of Sets Constraints
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Author : Alexander Aiken
language : en
Publisher:
Release Date : 1993
The Complexity Of Sets Constraints written by Alexander Aiken and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Complexity Of Constraints
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Author : Nadia Creignou
language : en
Publisher: Springer
Release Date : 2008-12-23
Complexity Of Constraints written by Nadia Creignou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-23 with Computers categories.
Nowadays constraint satisfaction problems (CSPs) are ubiquitous in many different areas of computer science, from artificial intelligence and database systems to circuit design, network optimization, and theory of programming languages. Consequently, it is important to analyze and pinpoint the computational complexity of certain algorithmic tasks related to constraint satisfaction. The complexity-theoretic results of these tasks may have a direct impact on, for instance, the design and processing of database query languages, or strategies in data-mining, or the design and implementation of planners. This state-of-the-art survey contains the papers that were invited by the organizers after conclusion of an International Dagstuhl-Seminar on Complexity of Constraints, held in Dagstuhl Castle, Germany, in October 2006. A number of speakers were solicited to write surveys presenting the state of the art in their area of expertise. These contributions were peer-reviewed by experts in the field and revised before they were collated to the 9 papers of this volume. In addition, the volume contains a reprint of a survey by Kolaitis and Vardi on the logical approach to constraint satisfaction that first appeared in 'Finite Model Theory and its Applications', published by Springer in 2007.
A Guide To Algorithm Design
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Author : Anne Benoit
language : en
Publisher: CRC Press
Release Date : 2013-08-27
A Guide To Algorithm Design written by Anne Benoit and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-27 with Computers categories.
Presenting a complementary perspective to standard books on algorithms, A Guide to Algorithm Design: Paradigms, Methods, and Complexity Analysis provides a roadmap for readers to determine the difficulty of an algorithmic problem by finding an optimal solution or proving complexity results. It gives a practical treatment of algorithmic complexity and guides readers in solving algorithmic problems. Divided into three parts, the book offers a comprehensive set of problems with solutions as well as in-depth case studies that demonstrate how to assess the complexity of a new problem. Part I helps readers understand the main design principles and design efficient algorithms. Part II covers polynomial reductions from NP-complete problems and approaches that go beyond NP-completeness. Part III supplies readers with tools and techniques to evaluate problem complexity, including how to determine which instances are polynomial and which are NP-hard. Drawing on the authors’ classroom-tested material, this text takes readers step by step through the concepts and methods for analyzing algorithmic complexity. Through many problems and detailed examples, readers can investigate polynomial-time algorithms and NP-completeness and beyond.
Logic And Computational Complexity
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Author : Daniel Leivant
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-08-02
Logic And Computational Complexity written by Daniel Leivant and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-02 with Computers categories.
This book contains revised versions of papers invited for presentation at the International Workshop on Logic and Computational Complexity, LCC '94, held in Indianapolis, IN in October 1994. The synergy between logic and computational complexity has gained importance and vigor in recent years, cutting across many areas. The 25 revised full papers in this book contributed by internationally outstanding researchers document the state-of-the-art in this interdisciplinary field of growing interest; they are presented in sections on foundational issues, applicative and proof-theoretic complexity, complexity of proofs, computational complexity of functionals, complexity and model theory, and finite model theory.