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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 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.
List of contents
Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The W-Hierarchy.- The A-Hierarchy.- Kernelization and Linear Programming Techniques.- The Automata-Theoretic Approach.- Tree Width.- Planarity and Bounded Local Tree Width.- Homomorphisms and Embeddings.- Parameterized Counting Problems.- Bounded Fixed-Parameter Tractability and Limited Nondeterminism.- Subexponential Fixed-Parameter Tractability.
Summary
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.
Additional text
From the reviews:
"The book is comprehensive and up-to-date. … The definitions are illustrated by good examples, the proofs are complete and proceed at a convenient pace, the connections and the implications of the results are spelled out clearly, the exercises are relevant. The book is recommended to specialists as a work of reference, as well as to beginners who want a solid introduction to the theory of parametrized computational problems." (Marius Zimand, Zentralblatt MATH, Vol. 1143, 2008)
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From the reviews:
"The book is comprehensive and up-to-date. ... The definitions are illustrated by good examples, the proofs are complete and proceed at a convenient pace, the connections and the implications of the results are spelled out clearly, the exercises are relevant. The book is recommended to specialists as a work of reference, as well as to beginners who want a solid introduction to the theory of parametrized computational problems." (Marius Zimand, Zentralblatt MATH, Vol. 1143, 2008)
