Parameterized Complexity

1. Front Matter

   Pages i-xv

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2. Computers, Complexity, and Intractability from the Parametric Point of View

   1. Computers, Complexity, and Intractability from the Parametric Point of View

      • R. G. Downey, M. R. Fellows

      Pages 1-20

3. Parameterized Tractability

   1. Front Matter

      Pages 21-21

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   2. The Basic Definitions

      • R. G. Downey, M. R. Fellows

      Pages 23-28

   3. Some Ad Hoc Methods: The Methods of Bounded Search Tree and Problem Kernel

      • R. G. Downey, M. R. Fellows

      Pages 29-48

   4. Optimization Problems, Approximation Schemes, and Their Relation with FPT

      • R. G. Downey, M. R. Fellows

      Pages 49-60

   5. The Advice View Revisited and LOGSPACE

      • R. G. Downey, M. R. Fellows

      Pages 61-66

   6. Methods via Automata and Bounded Treewidth

      • R. G. Downey, M. R. Fellows

      Pages 67-142

   7. Well-Quasi-Orderings and the Robertson-Seymour Theorems

      • R. G. Downey, M. R. Fellows

      Pages 143-209

   8. Miscellaneous Techniques

      • R. G. Downey, M. R. Fellows

      Pages 211-223

4. Parameterized Intractability

   1. Front Matter

      Pages 225-225

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   2. Reductions

      • R. G. Downey, M. R. Fellows

      Pages 227-234

   3. The Basic Class W[1] and an Analog of Cook’s Theorem

      • R. G. Downey, M. R. Fellows

      Pages 235-254

   4. Some Other W[1]-Hardness Results

      • R. G. Downey, M. R. Fellows

      Pages 255-281

   5. The W -Hierarchy

      • R. G. Downey, M. R. Fellows

      Pages 283-313

   6. Beyond W[t]-Hardness

      • R. G. Downey, M. R. Fellows

      Pages 315-330

   7. Fixed Parameter Analogs of PSPACE and k-Move Games

      • R. G. Downey, M. R. Fellows

      Pages 331-340

   8. Provable Intractability: The Class X P

      • R. G. Downey, M. R. Fellows

      Pages 341-350

5. Structural and Other Results

   1. Front Matter

      Pages 351-351

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   2. Another Basis for the W -Hierarchy, the Tradeoff-Theorem, and Randomized Reductions

      • R. G. Downey, M. R. Fellows

      Pages 353-362

The idea for this book was conceived over the second bottle of Villa Maria's Caber­ net Medot '89, at the dinner of the Australasian Combinatorics Conference held at Palmerston North, New Zealand in December 1990, where the authors first met and discovered they had a number of interests in common. Initially, we embarked on a small project to try to formulate reductions to address the apparent parame­ terized intractability of DOMINATING SET, and to introduce a structure in which to frame our answers. Having spent several months trying to get the definitions for the reductions right (they now seem so obvious), we turned to our tattered copies of Garey and Johnson's work [239]. We were stunned to find that virtually none of the classical reductions worked in the parameterized setting. We then wondered if we'd be able to find any interesting reductions. Several years, many more bottles, so many papers, and reductions later it [3] seemed that we had unwittingly stumbled upon what we believe is a truly central and new area of complexity theory. It seemed to us that the material would be of great interest to people working in areas where exact algorithms for a small range of parameters are natural and useful (e. g. , Molecular Biology, VLSI design). The tractability theory was rich with distinctive and powerful techniques. The intractability theory seemed to have a deep structure and techniques all of its own.

• Algorithms
• Automat
• Graph
• algorithm
• automata
• classification
• complexity
• complexity theory
• optimization
• combinatorics
• algorithm analysis and problem complexity

• Department of Mathematics, Victoria University, Wellington, Wellington, New Zealand

  R. G. Downey

• Department of Computer Science, University of Victoria, Victoria, Victoria, Canada

  M. R. Fellows

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