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Parameterized Complexity Theory

By J. Flum , M. Grohe

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  • ISBN13: 978-3-5402-9952-3
  • 507 Pages
  • User Level: Students
  • Publication Date: May 1, 2006
  • Available eBook Formats: PDF
Full 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.
Table of Contents

Table of Contents

  1. Fixed
  2. Parameter Tractability.
  3. Reductions and Parameterized Intractability.
  4. The Class W[P].
  5. Logic and Complexity.
  6. Two Fundamental Hierarchies.
  7. The First Level of the Hierarchies.
  8. The W
  9. Hierarchy.
  10. The A
  11. Hierarchy.
  12. Kernelization and Linear Programming Techniques.
  13. The Automata
  14. Theoretic Approach.
  15. Tree Width.
  16. Planarity and Bounded Local Tree Width.
  17. Homomorphisms and Embeddings.
  18. Parameterized Counting Problems.
  19. Bounded Fixed
  20. Parameter Tractability.
  21. Subexponential Fixed
  22. Parameter Tractability.
  23. Appendix, Background from Complexity Theory.
  24. References.
  25. Notation.
  26. Index.

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