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Parameterized Complexity

  • Book
  • © 1999

Overview

Authors:
  1. R. G. Downey

    1. Department of Mathematics, Victoria University, Wellington, Wellington, New Zealand

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  2. M. R. Fellows

    1. Department of Computer Science, University of Victoria, Victoria, Victoria, Canada

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  • This book presents an approach to complexity theory which offers a means of analyzing algorithms in terms of their tractability Downey considers problems in terms of parameterized languages and taking "k-slices" of the language, giving readers insight into new classes of algorithms which may be analyzed more precisely than before This book will be of great value to computer scientists and mathematicians interested in the design and analysis of algorithms

Part of the book series: Monographs in Computer Science (MCS)

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Table of contents (19 chapters)

  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
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Keywords

About this book

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.

Authors and Affiliations

  • 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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