Ebook: Parameterized Complexity Theory

Parameterized complexity theory is a recent branch of computational complexity theory that provides a framework for a refined analysis of hard algorithmic problems. The central notion of the theory, fixed-parameter tractability, has led to the development of various new algorithmic techniques and a whole new theory of intractability.

This book is a state-of-the-art introduction to both algorithmic techniques for fixed-parameter tractability and the structural theory of parameterized complexity classes, and it presents detailed proofs of recent advanced results that have not appeared in book form before. Several chapters are each devoted to intractability, algorithmic techniques for designing fixed-parameter tractable algorithms, and bounded fixed-parameter tractability and subexponential time complexity. The treatment is comprehensive, and the reader is supported with exercises, notes, a detailed index, and some background on complexity theory and logic.

The book will be of interest to computer scientists, mathematicians and graduate students engaged with algorithms and problem complexity.

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Parameterized complexity theory is a recent branch of computational complexity theory that provides a framework for a refined analysis of hard algorithmic problems. The central notion of the theory, fixed-parameter tractability, has led to the development of various new algorithmic techniques and a whole new theory of intractability.

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, and it presents detailed proofs of recent advanced results that have not appeared in book form before.

Several chapters each are devoted to intractability, algorithmic techniques for designing fixed-parameter tractable algorithms, and bounded fixed-parameter tractability and subexponential time complexity. The treatment is comprehensive, and the reader is supported with exercises, notes, a detailed index, and some background on complexity theory and logic.

The book will be of interest to computer scientists, mathematicians and graduate students engaged with algorithms and problem complexity.

---

Parameterized complexity theory is a recent branch of computational complexity theory that provides a framework for a refined analysis of hard algorithmic problems. The central notion of the theory, fixed-parameter tractability, has led to the development of various new algorithmic techniques and a whole new theory of intractability.

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, and it presents detailed proofs of recent advanced results that have not appeared in book form before.

Several chapters each are devoted to intractability, algorithmic techniques for designing fixed-parameter tractable algorithms, and bounded fixed-parameter tractability and subexponential time complexity. The treatment is comprehensive, and the reader is supported with exercises, notes, a detailed index, and some background on complexity theory and logic.

The book will be of interest to computer scientists, mathematicians and graduate students engaged with algorithms and problem complexity.

Content:
Front Matter....Pages I-XIII
Fixed-Parameter Tractability....Pages 1-31
Reductions and Parameterized Intractability....Pages 33-43
The Class W[P]....Pages 45-63
Logic and Complexity....Pages 65-93
Two Fundamental Hierarchies....Pages 95-103
The First Level of the Hierarchies....Pages 105-131
The W-Hierarchy....Pages 133-164
The A-Hierarchy....Pages 165-205
Kernelization and Linear Programming Techniques....Pages 207-231
The Automata-Theoretic Approach....Pages 233-260
Tree Width....Pages 261-299
Planarity and Bounded Local Tree Width....Pages 301-325
Homomorphisms and Embeddings....Pages 327-355
Parameterized Counting Problems....Pages 357-388
Bounded Fixed-Parameter Tractability and Limited Nondeterminism....Pages 389-416
Subexponential Fixed-Parameter Tractability....Pages 417-451
Back Matter....Pages 453-495

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Parameterized complexity theory is a recent branch of computational complexity theory that provides a framework for a refined analysis of hard algorithmic problems. The central notion of the theory, fixed-parameter tractability, has led to the development of various new algorithmic techniques and a whole new theory of intractability.

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, and it presents detailed proofs of recent advanced results that have not appeared in book form before.

Several chapters each are devoted to intractability, algorithmic techniques for designing fixed-parameter tractable algorithms, and bounded fixed-parameter tractability and subexponential time complexity. The treatment is comprehensive, and the reader is supported with exercises, notes, a detailed index, and some background on complexity theory and logic.

The book will be of interest to computer scientists, mathematicians and graduate students engaged with algorithms and problem complexity.

Content:
Front Matter....Pages I-XIII
Fixed-Parameter Tractability....Pages 1-31
Reductions and Parameterized Intractability....Pages 33-43
The Class W[P]....Pages 45-63
Logic and Complexity....Pages 65-93
Two Fundamental Hierarchies....Pages 95-103
The First Level of the Hierarchies....Pages 105-131
The W-Hierarchy....Pages 133-164
The A-Hierarchy....Pages 165-205
Kernelization and Linear Programming Techniques....Pages 207-231
The Automata-Theoretic Approach....Pages 233-260
Tree Width....Pages 261-299
Planarity and Bounded Local Tree Width....Pages 301-325
Homomorphisms and Embeddings....Pages 327-355
Parameterized Counting Problems....Pages 357-388
Bounded Fixed-Parameter Tractability and Limited Nondeterminism....Pages 389-416
Subexponential Fixed-Parameter Tractability....Pages 417-451
Back Matter....Pages 453-495
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