Parameterized Complexity Theory

Description

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. 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