Parameterized Complexity TheoryParameterized 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. |
Inhalt
| 1 | |
Reductions and Parameterized Intractability 33 | 32 |
The Class WP | 45 |
Logic and Complexity 65 | 64 |
Two Fundamental Hierarchies | 95 |
The First Level of the Hierarchies 105 | 104 |
The WHierarchy | 133 |
The AHierarchy | 165 |
Tree Width | 261 |
Planarity and Bounded Local Tree Width 301 | 300 |
Homomorphisms and Embeddings | 327 |
Parameterized Counting Problems 357 | 356 |
Bounded FixedParameter Tractability | 389 |
Subexponential FixedParameter Tractability | 417 |
Background from Complexity Theory | 453 |
References | 463 |
Kernelization and Linear Programming Techniques 207 | 206 |
The AutomataTheoretic Approach | 233 |
Notation 477 | 476 |