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Exact Exponential Algorithms

Author: Fedor V. Fomin

Publisher: Springer Science & Business Media

Published: 2010-10-26

Total Pages: 208

ISBN-13: 3642165338

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For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING.

Book Synopsis Exact Exponential Algorithms by : Fedor V. Fomin

Download or read book Exact Exponential Algorithms written by Fedor V. Fomin and published by Springer Science & Business Media. This book was released on 2010-10-26 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING.

STACS 2005

Author: Volker Diekert

Publisher: Springer

Published: 2005-02-02

Total Pages: 722

ISBN-13: 3540318569

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This book constitutes the refereed proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2005, held in Stuttgart, Germany in February 2005. The 54 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 217 submissions. A broad variety of topics from theoretical computer science are addressed, in particular complexity theory, algorithmics, computational discrete mathematics, automata theory, combinatorial optimization and approximation, networking and graph theory, computational geometry, grammar systems and formal languages, etc.

Book Synopsis STACS 2005 by : Volker Diekert

Download or read book STACS 2005 written by Volker Diekert and published by Springer. This book was released on 2005-02-02 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2005, held in Stuttgart, Germany in February 2005. The 54 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 217 submissions. A broad variety of topics from theoretical computer science are addressed, in particular complexity theory, algorithmics, computational discrete mathematics, automata theory, combinatorial optimization and approximation, networking and graph theory, computational geometry, grammar systems and formal languages, etc.

Graph-Theoretic Concepts in Computer Science

Author: Juraj Hromkovič

Publisher: Springer

Published: 2005-01-25

Total Pages: 413

ISBN-13: 3540305599

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During its 30-year existence, the International Workshop on Graph-Theoretic Concepts in Computer Science has become a distinguished and high-quality computer science event. The workshop aims at uniting theory and practice by demonstrating how graph-theoretic concepts can successfully be applied to v- ious areas of computer science and by exposing new theories emerging from applications. In this way, WG provides a common ground for the exchange of information among people dealing with several graph problems and working in various disciplines. Thereby, the workshop contributes to forming an interdis- plinary research community. The original idea of the Workshop on Graph-Theoretic Concepts in C- puter Science was ingenuity in all theoretical aspects and applications of graph concepts, wherever applied. Within the last ten years, the development has strengthened in particular the topic of structural graph properties in relation to computational complexity. This workshop has become pivotal for the c- munity interested in these areas.An aimspeci?c to the 30thWG was to support the central role of WG in both of the prementioned areas on the one hand and on the other hand to promote its originally broader scope. The 30th WG was held at the Physikzentrum Bad Honnef, which serves as the main meeting point of the German Physical Society. It o?ers a secluded setting for research conferences, seminars, and workshops, and has proved to be especiallystimulatingforfruitful discussions.Talksweregiveninthenewlecture hall with a modern double rear projection, interactive electronic board, and full video conferencing equipment.

Book Synopsis Graph-Theoretic Concepts in Computer Science by : Juraj Hromkovič

Download or read book Graph-Theoretic Concepts in Computer Science written by Juraj Hromkovič and published by Springer. This book was released on 2005-01-25 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: During its 30-year existence, the International Workshop on Graph-Theoretic Concepts in Computer Science has become a distinguished and high-quality computer science event. The workshop aims at uniting theory and practice by demonstrating how graph-theoretic concepts can successfully be applied to v- ious areas of computer science and by exposing new theories emerging from applications. In this way, WG provides a common ground for the exchange of information among people dealing with several graph problems and working in various disciplines. Thereby, the workshop contributes to forming an interdis- plinary research community. The original idea of the Workshop on Graph-Theoretic Concepts in C- puter Science was ingenuity in all theoretical aspects and applications of graph concepts, wherever applied. Within the last ten years, the development has strengthened in particular the topic of structural graph properties in relation to computational complexity. This workshop has become pivotal for the c- munity interested in these areas.An aimspeci?c to the 30thWG was to support the central role of WG in both of the prementioned areas on the one hand and on the other hand to promote its originally broader scope. The 30th WG was held at the Physikzentrum Bad Honnef, which serves as the main meeting point of the German Physical Society. It o?ers a secluded setting for research conferences, seminars, and workshops, and has proved to be especiallystimulatingforfruitful discussions.Talksweregiveninthenewlecture hall with a modern double rear projection, interactive electronic board, and full video conferencing equipment.

Graphical Models, Exponential Families, and Variational Inference

Author: Martin J. Wainwright

Publisher: Now Publishers Inc

Published: 2008

Total Pages: 324

ISBN-13: 1601981848

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The core of this paper is a general set of variational principles for the problems of computing marginal probabilities and modes, applicable to multivariate statistical models in the exponential family.

Book Synopsis Graphical Models, Exponential Families, and Variational Inference by : Martin J. Wainwright

Download or read book Graphical Models, Exponential Families, and Variational Inference written by Martin J. Wainwright and published by Now Publishers Inc. This book was released on 2008 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of this paper is a general set of variational principles for the problems of computing marginal probabilities and modes, applicable to multivariate statistical models in the exponential family.

Parameterized Algorithms

Author: Marek Cygan

Publisher: Springer

Published: 2015-07-20

Total Pages: 618

ISBN-13: 3319212753

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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 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.

Exponential Time Algorithms

Author: Serge Gaspers

Publisher: Serge Gaspers

Published: 2010-02

Total Pages: 207

ISBN-13: 3639218256

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This book studies exponential time algorithms for NP-hard problems. In this modern area, the aim is to design algorithms for combinatorially hard problems that execute provably faster than a brute-force enumeration of all candidate solutions. After an introduction and survey of the field, the text focuses first on the design and especially the analysis of branching algorithms. The analysis of these algorithms heavily relies on measures of the instances, which aim at capturing the structure of the instances, not merely their size. This makes them more appropriate to quantify the progress an algorithm makes in the process of solving a problem. Expanding the methodology to design exponential time algorithms, new techniques are then presented. Two of them combine treewidth based algorithms with branching or enumeration algorithms. Another one is the iterative compression technique, prominent in the design of parameterized algorithms, and adapted here to the design of exponential time algorithms. This book assumes basic knowledge of algorithms and should serve anyone interested in exactly solving hard problems.

Book Synopsis Exponential Time Algorithms by : Serge Gaspers

Download or read book Exponential Time Algorithms written by Serge Gaspers and published by Serge Gaspers. This book was released on 2010-02 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies exponential time algorithms for NP-hard problems. In this modern area, the aim is to design algorithms for combinatorially hard problems that execute provably faster than a brute-force enumeration of all candidate solutions. After an introduction and survey of the field, the text focuses first on the design and especially the analysis of branching algorithms. The analysis of these algorithms heavily relies on measures of the instances, which aim at capturing the structure of the instances, not merely their size. This makes them more appropriate to quantify the progress an algorithm makes in the process of solving a problem. Expanding the methodology to design exponential time algorithms, new techniques are then presented. Two of them combine treewidth based algorithms with branching or enumeration algorithms. Another one is the iterative compression technique, prominent in the design of parameterized algorithms, and adapted here to the design of exponential time algorithms. This book assumes basic knowledge of algorithms and should serve anyone interested in exactly solving hard problems.

Combinatorial Optimization -- Eureka, You Shrink!

Author: Michael Jünger

Publisher: Springer

Published: 2003-07-01

Total Pages: 219

ISBN-13: 3540364781

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This book is dedicated to Jack Edmonds in appreciation of his ground breaking work that laid the foundations for a broad variety of subsequent results achieved in combinatorial optimization.The main part consists of 13 revised full papers on current topics in combinatorial optimization, presented at Aussois 2001, the Fifth Aussois Workshop on Combinatorial Optimization, March 5-9, 2001, and dedicated to Jack Edmonds.Additional highlights in this book are an account of an Aussois 2001 special session dedicated to Jack Edmonds including a speech given by William R. Pulleyblank as well as newly typeset versions of three up-to-now hardly accessible classical papers:- Submodular Functions, Matroids, and Certain Polyhedranbsp;nbsp; by Jack Edmonds- Matching: A Well-Solved Class of Integer Linear Programsnbsp;nbsp; by Jack Edmonds and Ellis L. Johnson- Theoretical Improvements in Algorithmic Efficiency for Network Flow Problemsnbsp;nbsp; by Jack Edmonds and Richard M. Karp.

Book Synopsis Combinatorial Optimization -- Eureka, You Shrink! by : Michael Jünger

Download or read book Combinatorial Optimization -- Eureka, You Shrink! written by Michael Jünger and published by Springer. This book was released on 2003-07-01 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to Jack Edmonds in appreciation of his ground breaking work that laid the foundations for a broad variety of subsequent results achieved in combinatorial optimization.The main part consists of 13 revised full papers on current topics in combinatorial optimization, presented at Aussois 2001, the Fifth Aussois Workshop on Combinatorial Optimization, March 5-9, 2001, and dedicated to Jack Edmonds.Additional highlights in this book are an account of an Aussois 2001 special session dedicated to Jack Edmonds including a speech given by William R. Pulleyblank as well as newly typeset versions of three up-to-now hardly accessible classical papers:- Submodular Functions, Matroids, and Certain Polyhedranbsp;nbsp; by Jack Edmonds- Matching: A Well-Solved Class of Integer Linear Programsnbsp;nbsp; by Jack Edmonds and Ellis L. Johnson- Theoretical Improvements in Algorithmic Efficiency for Network Flow Problemsnbsp;nbsp; by Jack Edmonds and Richard M. Karp.

The Steiner Tree Problem

Author: F.K. Hwang

Publisher: Elsevier

Published: 1992-10-20

Total Pages: 336

ISBN-13: 9780080867939

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The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues. This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging. The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole.

Book Synopsis The Steiner Tree Problem by : F.K. Hwang

Download or read book The Steiner Tree Problem written by F.K. Hwang and published by Elsevier. This book was released on 1992-10-20 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues. This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging. The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole.

Invitation to Fixed-Parameter Algorithms

Author: Rolf Niedermeier

Publisher: OUP Oxford

Published: 2006-02-02

Total Pages: 316

ISBN-13: 0191524158

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This research-level text is an application-oriented introduction to the growing and highly topical area of the development and analysis of efficient fixed-parameter algorithms for optimally solving computationally hard combinatorial problems. The book is divided into three parts: a broad introduction that provides the general philosophy and motivation; followed by coverage of algorithmic methods developed over the years in fixed-parameter algorithmics forming the core of the book; and a discussion of the essentials from parameterized hardness theory with a focus on W[1]-hardness which parallels NP-hardness, then stating some relations to polynomial-time approximation algorithms, and finishing up with a list of selected case studies to show the wide range of applicability of the presented methodology. Aimed at graduate and research mathematicians, programmers, algorithm designers, and computer scientists, the book introduces the basic techniques and results and provides a fresh view on this highly innovative field of algorithmic research.

Book Synopsis Invitation to Fixed-Parameter Algorithms by : Rolf Niedermeier

Download or read book Invitation to Fixed-Parameter Algorithms written by Rolf Niedermeier and published by OUP Oxford. This book was released on 2006-02-02 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research-level text is an application-oriented introduction to the growing and highly topical area of the development and analysis of efficient fixed-parameter algorithms for optimally solving computationally hard combinatorial problems. The book is divided into three parts: a broad introduction that provides the general philosophy and motivation; followed by coverage of algorithmic methods developed over the years in fixed-parameter algorithmics forming the core of the book; and a discussion of the essentials from parameterized hardness theory with a focus on W[1]-hardness which parallels NP-hardness, then stating some relations to polynomial-time approximation algorithms, and finishing up with a list of selected case studies to show the wide range of applicability of the presented methodology. Aimed at graduate and research mathematicians, programmers, algorithm designers, and computer scientists, the book introduces the basic techniques and results and provides a fresh view on this highly innovative field of algorithmic research.

Finite Difference Computing with Exponential Decay Models

Author: Hans Petter Langtangen

Publisher: Springer

Published: 2016-06-10

Total Pages: 210

ISBN-13: 3319294393

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This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular.

Book Synopsis Finite Difference Computing with Exponential Decay Models by : Hans Petter Langtangen

Download or read book Finite Difference Computing with Exponential Decay Models written by Hans Petter Langtangen and published by Springer. This book was released on 2016-06-10 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular.