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E-grāmata: Parameterized Complexity

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  • Formāts: PDF+DRM
  • Sērija : Monographs in Computer Science
  • Izdošanas datums: 06-Dec-2012
  • Izdevniecība: Springer-Verlag New York Inc.
  • Valoda: eng
  • ISBN-13: 9781461205159
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Parameterized ComplexityPalielināt
  • Formāts: PDF+DRM
  • Sērija : Monographs in Computer Science
  • Izdošanas datums: 06-Dec-2012
  • Izdevniecība: Springer-Verlag New York Inc.
  • Valoda: eng
  • ISBN-13: 9781461205159
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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.

Papildus informācija

Springer Book Archives
1 Computers, Complexity, and Intractability from the Parametric Point of
View.- 1.1 Introduction.- 1.2 The Role of Computational Complexity in Modern
Science.- 1.3 The Story of Dr.O, Continued.- 1.4 Reworking the Foundations of
Computational Complexity.- 1.5 A Deal with the Devil.- 1.6 How Parameters
Arise in Practice.- 1.7 A Distinctive Positive Toolkit.- 1.8 O No?.- 1.9 The
Barometer of Parametric Intractability.- 1.10 Structural Aspects of
Parameterized Complexity.- 1.11 An Overview of Current Research Horizons.- I
Parameterized Tractability.- 2 The Basic Definitions.- 3 Some Ad Hoc Methods:
The Methods of Bounded Search Tree and Problem Kernel.- 4 Optimization
Problems, Approximation Schemes, and Their Relation with FPT.- 5 The Advice
View Revisited and LOGSPACE.- 6 Methods via Automata and Bounded Treewidth.-
7 Well-Quasi-Orderings and the Robertson-Seymour Theorems.- 8 Miscellaneous
Techniques.- II Parameterized Intractability.- 9 Reductions.- 10 The Basic
Class W[ 1] and an Analog of Cooks Theorem.- 11 Some Other W[ 1]-Hardness
Results.- 12 The W -Hierarchy.- 13 Beyond W[ t]-Hardness.- 14 Fixed Parameter
Analogs of PSPACE and k-Move Games.- 15 Provable Intractability: The Class
XP.- III Structural and Other Results.- 16 Another Basis for the W
-Hierarchy, the Tradeoff-Theorem, and Randomized Reductions.- 17
Relationships with Classical Complexity and Limited Nondeterminism.- 18 The
Monotone and Antimonotone Collapse Theorems: MONOTONEW[ 2t + 1] = W[ 2t] and
ANTIMONOTONEW[ 2t + 2] = W[ 2t + 1].- 19 The Structure of Languages Under
Parameterized Reducibilities.- IV Appendix.- A A Problem Compendium and Guide
to W-Hierarchy Completeness, Hardness, and Classification; and Some Research
Horizons.- B Research Horizons.- B.2 A Lineup of Tough Customers.- B.3
ConnectionsBetween Classical and Parameterized Complexity.- B.4
Classification Gaps.- B.5 Structural Issues and Analogs of Classical
Results.- References.
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