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The Resource Fundamentals of parameterized complexity, Rodney G. Downey, Michael R. Fellows

Fundamentals of parameterized complexity, Rodney G. Downey, Michael R. Fellows

Creator
Author
Contributor
Summary
The field of parameterized complexity/multivariate complexity algorithmics is an exciting and vibrant part of theoretical computer science, responding to the vital need for efficient algorithms in modern society. 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. Topics and 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 This classroom-tested and easy-to-follow textbook/reference is essential reading for the beginning graduate student and advanced undergraduate student. The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research
Language
eng
Work
Publication
Extent
1 online resource (848 pages)
Contents
  • Further Elementary Techniques
  • Color Coding, Multilinear Detection, and Randomized Divide and Conquer
  • Optimization Problems, Approximation Schemes, and Their Relation to FPT
  • Techniques Based on Graph Structure.
  • Treewidth and Dynamic Programming
  • Heuristics for Treewidth
  • Methods via Automata and Bounded Treewidth
  • Courcelle's Theorem
  • More on Width-Metrics: Applications and Local Treewidth
  • Depth-First Search and the Plehn-Voigt Theorem
  • Parameterized Tractability.
  • Other Width Metrics
  • Exotic Meta-techniques.
  • Well-Quasi-Orderings and the Robertson-Seymour Theorems
  • The Graph Minor Theorem
  • Applications of the Obstruction Principle and WQOs
  • Hardness Theory.
  • Reductions
  • The Basic Class W[1] and an Analog of Cook's Theorem
  • Some Other W[1] Hardness Results
  • The W-Hierarchy
  • Preliminaries
  • The Monotone and Antimonotone Collapse Theorems: Monotone W[2t+1]=W[2t] and Antimonotone W[2t+2]=W[2t+1]
  • Beyond W[t]-Hardness
  • Fixed Parameter Analogues of PSpace and k-Move Games
  • Provable Intractability: The Class XP
  • Another Basis for the W-Hierarchy and the Tradeoff Theorem
  • Approximations, Connections, Lower Bounds.
  • The M-Hierarchy, and XP-Optimality
  • Kernelization Lower Bounds
  • Further Topics.
  • Parameterized Approximation
  • The Basic Definitions
  • Parameterized Counting and Randomization
  • Research Horizons.
  • Research Horizons
  • Appendices.
  • Appendix 1:
  • Network Flows and Matchings
  • --
  • Appendix 2:
  • Menger's Theorems
  • Elementary Positive Techniques.
  • Bounded Search Trees
  • Kernelization
  • More on Kernelization
  • Iterative Compression, and Measure and Conquer, for Minimization Problems
Isbn
9781447155591
Instance
Label
Fundamentals of parameterized complexity
Title
Fundamentals of parameterized complexity
Statement of responsibility
Rodney G. Downey, Michael R. Fellows
Creator
Contributor
Author
Subject
Language
eng
Summary
The field of parameterized complexity/multivariate complexity algorithmics is an exciting and vibrant part of theoretical computer science, responding to the vital need for efficient algorithms in modern society. 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. Topics and 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 This classroom-tested and easy-to-follow textbook/reference is essential reading for the beginning graduate student and advanced undergraduate student. The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Downey, R. G.
Dewey number
005.1
Illustrations
illustrations
Index
no index present
LC call number
QA76.9.A43
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorDate
1952-
http://library.link/vocab/relatedWorkOrContributorName
Fellows, M. R.
Series statement
Texts in Computer Science
http://library.link/vocab/subjectName
  • Computer algorithms
  • Computer science
  • Computer algorithms
  • Computer science
Label
Fundamentals of parameterized complexity, Rodney G. Downey, Michael R. Fellows
Instantiates
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Further Elementary Techniques
  • Color Coding, Multilinear Detection, and Randomized Divide and Conquer
  • Optimization Problems, Approximation Schemes, and Their Relation to FPT
  • Techniques Based on Graph Structure.
  • Treewidth and Dynamic Programming
  • Heuristics for Treewidth
  • Methods via Automata and Bounded Treewidth
  • Courcelle's Theorem
  • More on Width-Metrics: Applications and Local Treewidth
  • Depth-First Search and the Plehn-Voigt Theorem
  • Parameterized Tractability.
  • Other Width Metrics
  • Exotic Meta-techniques.
  • Well-Quasi-Orderings and the Robertson-Seymour Theorems
  • The Graph Minor Theorem
  • Applications of the Obstruction Principle and WQOs
  • Hardness Theory.
  • Reductions
  • The Basic Class W[1] and an Analog of Cook's Theorem
  • Some Other W[1] Hardness Results
  • The W-Hierarchy
  • Preliminaries
  • The Monotone and Antimonotone Collapse Theorems: Monotone W[2t+1]=W[2t] and Antimonotone W[2t+2]=W[2t+1]
  • Beyond W[t]-Hardness
  • Fixed Parameter Analogues of PSpace and k-Move Games
  • Provable Intractability: The Class XP
  • Another Basis for the W-Hierarchy and the Tradeoff Theorem
  • Approximations, Connections, Lower Bounds.
  • The M-Hierarchy, and XP-Optimality
  • Kernelization Lower Bounds
  • Further Topics.
  • Parameterized Approximation
  • The Basic Definitions
  • Parameterized Counting and Randomization
  • Research Horizons.
  • Research Horizons
  • Appendices.
  • Appendix 1:
  • Network Flows and Matchings
  • --
  • Appendix 2:
  • Menger's Theorems
  • Elementary Positive Techniques.
  • Bounded Search Trees
  • Kernelization
  • More on Kernelization
  • Iterative Compression, and Measure and Conquer, for Minimization Problems
Control code
865474474
Dimensions
unknown
Extent
1 online resource (848 pages)
File format
unknown
Form of item
online
Isbn
9781447155591
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4471-5559-1
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)865474474
Label
Fundamentals of parameterized complexity, Rodney G. Downey, Michael R. Fellows
Publication
Antecedent source
unknown
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Further Elementary Techniques
  • Color Coding, Multilinear Detection, and Randomized Divide and Conquer
  • Optimization Problems, Approximation Schemes, and Their Relation to FPT
  • Techniques Based on Graph Structure.
  • Treewidth and Dynamic Programming
  • Heuristics for Treewidth
  • Methods via Automata and Bounded Treewidth
  • Courcelle's Theorem
  • More on Width-Metrics: Applications and Local Treewidth
  • Depth-First Search and the Plehn-Voigt Theorem
  • Parameterized Tractability.
  • Other Width Metrics
  • Exotic Meta-techniques.
  • Well-Quasi-Orderings and the Robertson-Seymour Theorems
  • The Graph Minor Theorem
  • Applications of the Obstruction Principle and WQOs
  • Hardness Theory.
  • Reductions
  • The Basic Class W[1] and an Analog of Cook's Theorem
  • Some Other W[1] Hardness Results
  • The W-Hierarchy
  • Preliminaries
  • The Monotone and Antimonotone Collapse Theorems: Monotone W[2t+1]=W[2t] and Antimonotone W[2t+2]=W[2t+1]
  • Beyond W[t]-Hardness
  • Fixed Parameter Analogues of PSpace and k-Move Games
  • Provable Intractability: The Class XP
  • Another Basis for the W-Hierarchy and the Tradeoff Theorem
  • Approximations, Connections, Lower Bounds.
  • The M-Hierarchy, and XP-Optimality
  • Kernelization Lower Bounds
  • Further Topics.
  • Parameterized Approximation
  • The Basic Definitions
  • Parameterized Counting and Randomization
  • Research Horizons.
  • Research Horizons
  • Appendices.
  • Appendix 1:
  • Network Flows and Matchings
  • --
  • Appendix 2:
  • Menger's Theorems
  • Elementary Positive Techniques.
  • Bounded Search Trees
  • Kernelization
  • More on Kernelization
  • Iterative Compression, and Measure and Conquer, for Minimization Problems
Control code
865474474
Dimensions
unknown
Extent
1 online resource (848 pages)
File format
unknown
Form of item
online
Isbn
9781447155591
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-1-4471-5559-1
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)865474474

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