Parameterized Complexity Theory

Parameterized Complexity Theory

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.

Author: J. Flum

Publisher: Springer Science & Business Media

ISBN: 354029953X

Category: Computers

Page: 495

View: 122

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.
Categories: Computers

Parameterized Complexity in the Polynomial Hierarchy

Parameterized Complexity in the Polynomial Hierarchy

This work extends the theory of parameterized complexity to higher levels of the Polynomial Hierarchy (PH).

Author: Ronald de Haan

Publisher: Springer Nature

ISBN: 9783662606704

Category: Mathematics

Page: 398

View: 364

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.
Categories: Mathematics

Parameterized Complexity

Parameterized Complexity

The book is as self-contained as possible and includes a great deal of background material.

Author: Rodney G. Downey

Publisher: Springer Science & Business Media

ISBN: 9781461205159

Category: Computers

Page: 533

View: 805

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.
Categories: Computers

Fundamentals of Parameterized Complexity

Fundamentals of Parameterized Complexity

The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research.

Author: Rodney G. Downey

Publisher: Springer Science & Business Media

ISBN: 9781447155591

Category: Computers

Page: 763

View: 821

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.
Categories: Computers

Parameterized and Exact Computation

Parameterized and Exact Computation

(Texas A&M University), Erik Demaine (MIT), and Stephan Kreutzer (Oxford University) for their contribution to the program of the workshop and their contributions for this proceedings volume.

Author: Martin Grohe

Publisher: Springer Science & Business Media

ISBN: 9783540797227

Category: Computers

Page: 227

View: 606

This book constitutes the refereed proceedings of the Third International Workshop on Parameterized and Exact Computation, IWPEC 2008, held in Victoria, Canada, in May 2008 - co-located with the 40th ACM Symposium on Theory of Computing, STOC 2008. The 17 revised full papers presented together with 3 invited lectures were carefully reviewed and selected from 32 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, parameterized complexity theory, relationship between parameterized complexity and traditional complexity classifications, applications of parameterized computation, implementation and experiments, high-performance computing and fixed-parameter tractability.
Categories: Computers

Parameterized and Exact Computation

Parameterized and Exact Computation

This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Symposium on Parameterized and Exact Computation, IPEC 2013, in Sophia Antipolis, France, in September 2013.

Author: Gregory Gutin

Publisher: Springer

ISBN: 9783319038988

Category: Computers

Page: 375

View: 158

This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Symposium on Parameterized and Exact Computation, IPEC 2013, in Sophia Antipolis, France, in September 2013. The 29 revised full papers presented were carefully reviewed and selected from 58 submissions. The topics addressed cover research in all aspects of parameterized/exact algorithms and complexity including but are 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.
Categories: Computers

Vertex Cover

Vertex Cover

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.

Author: Lambert M. Surhone

Publisher:

ISBN: 6130356528

Category: Mathematics

Page: 104

View: 857

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the mathematical discipline of graph theory, a vertex cover of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The problem of finding a minimum vertex cover is a classical optimization problem in computer science and is a typical example of an NP-hard optimization problem that has an approximation algorithm. Its decision version, the vertex cover problem was one of Karp's 21 NP-complete problems and is therefore a classical NP-complete problem in computational complexity theory. Furthermore, the vertex cover problem is fixed-parameter tractable and a central problem in parameterized complexity theory. The minimum vertex cover problem can be formulated as a half-integral linear program whose dual linear program is the maximum matching problem.
Categories: Mathematics

Parameterized and Exact Computation

Parameterized and Exact Computation

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.

Author: Dániel Marx

Publisher: Springer Science & Business Media

ISBN: 9783642280498

Category: Computers

Page: 273

View: 451

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.
Categories: Computers

Parameterized and Exact Computation

Parameterized and Exact Computation

Here are the refereed proceedings of the Second International Workshop on Parameterized and Exact Computation, IWPEC 2006, held in the context of the combined conference ALGO 2006.

Author: Hans L. Bodlaender

Publisher: Springer Science & Business Media

ISBN: 9783540390985

Category: Computers

Page: 277

View: 747

This book constitutes the refereed proceedings of the Second International Workshop on Parameterized and Exact Computation, IWPEC 2006, held in Zurich, Switzerland, in September 2006 in the context of the combined conference ALGO 2006. The 23 revised full papers presented together with 2 invited lectures were carefully reviewed and selected from numerous 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, parameterized complexity theory, relationships between parameterized complexity and traditional complexity, applications of parameterized and exact computation, implementation issues and high-performance computing.
Categories: Computers

Classic graph problems made temporal a parameterized complexity analysis

Classic graph problems made temporal     a parameterized complexity analysis

Molter, Hendrik. [FG06] J. Flum and M. Grohe. Parameterized Complexity Theory.
Vol. XIV. Texts in Theoretical Computer Science. An EATCS Series. Springer,
2006 (cited on p. 12). [Flu+17] T. Fluschnik, M. Hatzel, S. Härtlein, H. Molter, and
H.

Author: Molter, Hendrik

Publisher: Universitätsverlag der TU Berlin

ISBN: 9783798331723

Category: Computers

Page: 227

View: 444

This thesis investigates the parameterized computational complexity of six classic graph problems lifted to a temporal setting. More specifically, we consider problems defined on temporal graphs, that is, a graph where the edge set may change over a discrete time interval, while the vertex set remains unchanged. Temporal graphs are well-suited to model dynamic data and hence they are naturally motivated in contexts where dynamic changes or time-dependent interactions play an important role, such as, for example, communication networks, social networks, or physical proximity networks. The most important selection criteria for our problems was that they are well-motivated in the context of dynamic data analysis. Since temporal graphs are mathematically more complex than static graphs, it is maybe not surprising that all problems we consider in this thesis are NP-hard. We focus on the development of exact algorithms, where our goal is to obtain fixed-parameter tractability results, and refined computational hardness reductions that either show NP-hardness for very restricted input instances or parameterized hardness with respect to “large” parameters. In the context of temporal graphs, we mostly consider structural parameters of the underlying graph, that is, the graph obtained by ignoring all time information. However, we also consider parameters of other types, such as ones trying to measure how fast the temporal graph changes over time. In the following we briefly discuss the problem setting and the main results. Restless Temporal Paths. A path in a temporal graph has to respect causality, or time, which means that the edges used by a temporal path have to appear at non-decreasing times. We investigate temporal paths that additionally have a maximum waiting time in every vertex of the temporal graph. Our main contributions are establishing NP-hardness for the problem of finding restless temporal paths even in very restricted cases, and showing W[1]-hardness with respect to the feedback vertex number of the underlying graph. Temporal Separators. A temporal separator is a vertex set that, when removed from the temporal graph, destroys all temporal paths between two dedicated vertices. Our contribution here is twofold: Firstly, we investigate the computational complexity of finding temporal separators in temporal unit interval graphs, a generalization of unit interval graphs to the temporal setting. We show that the problem is NP-hard on temporal unit interval graphs but we identify an additional restriction which makes the problem solvable in polynomial time. We use the latter result to develop a fixed-parameter algorithm with a “distance-to-triviality” parameterization. Secondly, we show that finding temporal separators that destroy all restless temporal paths is Σ-P-2-hard. Temporal Matchings. We introduce a model for matchings in temporal graphs, where, if two vertices are matched at some point in time, then they have to “recharge” afterwards, meaning that they cannot be matched again for a certain number of time steps. In our main result we employ temporal line graphs to show that finding matchings is NP-hard even on instances where the underlying graph is a path. Temporal Coloring. We lift the classic graph coloring problem to the temporal setting. In our model, every edge has to be colored properly (that is,the endpoints are colored differently) at least once in every time interval of a certain length. We show that this problem is NP-hard in very restricted cases, even if we only have two colors. We present simple exponential-time algorithms to solve this problem. As a main contribution, we show that these algorithms presumably cannot be improved significantly. Temporal Cliques and s-Plexes. We propose a model for temporal s-plexes that is a canonical generalization of an existing model for temporal cliques. Our main contribution is a fixed-parameter algorithm that enumerates all maximal temporal s-plexes in a given temporal graph, where we use a temporal adaptation of degeneracy as a parameter. Temporal Cluster Editing. We present a model for cluster editing in temporal graphs, where we want to edit all “layers” of a temporal graph into cluster graphs that are sufficiently similar. Our main contribution is a fixed-parameter algorithm with respect to the parameter “number of edge modifications” plus the “measure of similarity” of the resulting clusterings. We further show that there is an efficient preprocessing procedure that can provably reduce the size of the input instance to be independent of the number of vertices of the original input instance.
Categories: Computers

Kernelization

Kernelization

Written by a team of experts in the field, this book introduces a rapidly developing area of preprocessing analysis known as kernelization.

Author: Fedor V. Fomin

Publisher: Cambridge University Press

ISBN: 9781108577335

Category: Computers

Page:

View: 865

Preprocessing, or data reduction, is a standard technique for simplifying and speeding up computation. Written by a team of experts in the field, this book introduces a rapidly developing area of preprocessing analysis known as kernelization. The authors provide an overview of basic methods and important results, with accessible explanations of the most recent advances in the area, such as meta-kernelization, representative sets, polynomial lower bounds, and lossy kernelization. The text is divided into four parts, which cover the different theoretical aspects of the area: upper bounds, meta-theorems, lower bounds, and beyond kernelization. The methods are demonstrated through extensive examples using a single data set. Written to be self-contained, the book only requires a basic background in algorithmics and will be of use to professionals, researchers and graduate students in theoretical computer science, optimization, combinatorics, and related fields.
Categories: Computers

The Multivariate Algorithmic Revolution and Beyond

The Multivariate Algorithmic Revolution and Beyond

The volume contains several surveys that introduce the reader to the field of parameterized complexity and discuss important notions, results, and developments in this field.

Author: Hans L. Bodlaender

Publisher: Springer

ISBN: 9783642308918

Category: Computers

Page: 506

View: 899

Parameterized complexity is currently a thriving field in complexity theory and algorithm design. A significant part of the success of the field can be attributed to Michael R. Fellows. This Festschrift has been published in honor of Mike Fellows on the occasion of his 60th birthday. It contains 20 papers that showcase the important scientific contributions of this remarkable man, describes the history of the field of parameterized complexity, and also reflects on other parts of Mike Fellows’s unique and broad range of interests, including his work on the popularization of discrete mathematics for young children. The volume contains several surveys that introduce the reader to the field of parameterized complexity and discuss important notions, results, and developments in this field.
Categories: Computers

Computational Complexity of some Optimization Problems in Planning

Computational Complexity of some Optimization Problems in Planning

The reason behind this is not only to differentiate between easy and hard planning instances, but also to use polynomial-time solvable instances in order to construct better heuristic functions and improve planners.

Author: Meysam Aghighi

Publisher: Linköping University Electronic Press

ISBN: 9789176855195

Category:

Page: 35

View: 334

Automated planning is known to be computationally hard in the general case. Propositional planning is PSPACE-complete and first-order planning is undecidable. One method for analyzing the computational complexity of planning is to study restricted subsets of planning instances, with the aim of differentiating instances with varying complexity. We use this methodology for studying the computational complexity of planning. Finding new tractable (i.e. polynomial-time solvable) problems has been a particularly important goal for researchers in the area. The reason behind this is not only to differentiate between easy and hard planning instances, but also to use polynomial-time solvable instances in order to construct better heuristic functions and improve planners. We identify a new class of tractable cost-optimal planning instances by restricting the causal graph. We study the computational complexity of oversubscription planning (such as the net-benefit problem) under various restrictions and reveal strong connections with classical planning. Inspired by this, we present a method for compiling oversubscription planning problems into the ordinary plan existence problem. We further study the parameterized complexity of cost-optimal and net-benefit planning under the same restrictions and show that the choice of numeric domain for the action costs has a great impact on the parameterized complexity. We finally consider the parameterized complexity of certain problems related to partial-order planning. In some applications, less restricted plans than total-order plans are needed. Therefore, a partial-order plan is being used instead. When dealing with partial-order plans, one important question is how to achieve optimal partial order plans, i.e. having the highest degree of freedom according to some notion of flexibility. We study several optimization problems for partial-order plans, such as finding a minimum deordering or reordering, and finding the minimum parallel execution length.
Categories:

Cognition and Intractability

Cognition and Intractability

Provides an accessible introduction to computational complexity analysis and its application to questions of intractability in cognitive science.

Author: Iris van Rooij

Publisher: Cambridge University Press

ISBN: 9781107043992

Category: Mathematics

Page: 386

View: 285

Provides an accessible introduction to computational complexity analysis and its application to questions of intractability in cognitive science.
Categories: Mathematics

Parameterized and Exact Computation

Parameterized and Exact Computation

Annotation. This book constitutes the refereed best selected papers of the 5th International Symposium on Parameterized and Exact Computation, IPEC 2010, held in Chennai, India, in December 2010.

Author: Venkatesh Raman

Publisher:

ISBN: OCLC:846900410

Category: Computational complexity

Page:

View: 279

Annotation. This book constitutes the refereed best selected papers of the 5th International Symposium on Parameterized and Exact Computation, IPEC 2010, held in Chennai, India, in December 2010. The 19 revised full papers presented were carefully reviewed and selected from 32 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; parameterized complexity theory; relationship between parameterized complexity and traditional complexity classifications; applications of parameterized and exact computation; implementation issues of parameterized and exact algorithms; fixed-parameter approximation; fast approximation in exponential time; kernelization lower and upper bounds.
Categories: Computational complexity

Descriptive Complexity

Descriptive Complexity

This book is a relatively self-contained introduction to the subject, which includes the necessary background material, as well as numerous examples and exercises.

Author: Neil Immerman

Publisher: Springer Science & Business Media

ISBN: 0387986006

Category: Computers

Page: 268

View: 822

By virtue of the close relationship between logic and relational databases, it turns out that complexity has important applications to databases such as analyzing the parallel time needed to compute a query, and the analysis of nondeterministic classes. This book is a relatively self-contained introduction to the subject, which includes the necessary background material, as well as numerous examples and exercises.
Categories: Computers

IJCAI 05

IJCAI 05

Parameterized complexity . The abundance of negative compilability results
mirrors a state of affairs in complexity theory : although many problems of interest
can be classified according to the developed scheme of complexity classes ( P ,
NP ...

Author: Leslie Pack Kaelbling

Publisher:

ISBN: UCSD:31822030088785

Category: Artificial intelligence

Page: 1779

View: 950

Categories: Artificial intelligence

Parameterized and Exact Computation

Parameterized and Exact Computation

1 Introduction Parameterized complexity theory provides a framework for a
refined complexity analysis of algorithmic problems that are intractable in general
. Central to the theory is the notion of fixed - parameter tractability , which relaxes
the ...

Author:

Publisher:

ISBN: UOM:39015061764224

Category: Computational complexity

Page:

View: 468

Categories: Computational complexity

SIAM Journal on Computing

SIAM Journal on Computing

We develop a parameterized complexity theory for counting problems . As the
basis of this theory , we introduce a hierarchy of parameterized counting
complexity classes # W [ t ] , for t > 1 , that corresponds to Downey and Fellows ' s
W ...

Author: Society for Industrial and Applied Mathematics

Publisher:

ISBN: UOM:39015058897573

Category: Automation

Page:

View: 948

Categories: Automation

Combinatorial Optimization and Graph Algorithms

Combinatorial Optimization and Graph Algorithms

Covering network designs, discrete convex analysis, facility location and clustering problems, matching games, and parameterized complexity, this book discusses theoretical aspects of combinatorial optimization and graph algorithms.

Author: Takuro Fukunaga

Publisher: Springer

ISBN: 9789811061479

Category: Computers

Page: 120

View: 206

Covering network designs, discrete convex analysis, facility location and clustering problems, matching games, and parameterized complexity, this book discusses theoretical aspects of combinatorial optimization and graph algorithms. Contributions are by renowned researchers who attended NII Shonan meetings on this essential topic. The collection contained here provides readers with the outcome of the authors’ research and productive meetings on this dynamic area, ranging from computer science and mathematics to operations research. Networks are ubiquitous in today's world: the Web, online social networks, and search-and-query click logs can lead to a graph that consists of vertices and edges. Such networks are growing so fast that it is essential to design algorithms to work for these large networks. Graph algorithms comprise an area in computer science that works to design efficient algorithms for networks. Here one can work on theoretical or practical problems where implementation of an algorithm for large networks is needed. In two of the chapters, recent results in graph matching games and fixed parameter tractability are surveyed. Combinatorial optimization is an intersection of operations research and mathematics, especially discrete mathematics, which deals with new questions and new problems, attempting to find an optimum object from a finite set of objects. Most problems in combinatorial optimization are not tractable (i.e., NP-hard). Therefore it is necessary to design an approximation algorithm for them. To tackle these problems requires the development and combination of ideas and techniques from diverse mathematical areas including complexity theory, algorithm theory, and matroids as well as graph theory, combinatorics, convex and nonlinear optimization, and discrete and convex geometry. Overall, the book presents recent progress in facility location, network design, and discrete convex analysis.
Categories: Computers