Fundamentals of parameterized complexity

著者

• Downey, R. G. (Rod G.)
• Fellows, Michael R.

書誌事項

Fundamentals of parameterized complexity

Rodney G. Downey, Michael R. Fellows

（Texts in computer science）

Springer, c2013

• : pbk

注記

Includes bibliographical references and index

内容説明・目次

内容説明

This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years.

目次

Introduction Part I: Parameterized Tractability Preliminaries The Basic Definitions Part II: Elementary Positive Techniques Bounded Search Trees Kernelization More on Kernelization Iterative Compression, and Measure and Conquer, for Minimization Problems Further Elementary Techniques Colour Coding, Multilinear Detection, and Randomized Divide and Conquer Optimization Problems, Approximation Schemes, and Their Relation to FPT Part III: Techniques Based on Graph Structure Treewidth and Dynamic Programming Heuristics for Treewidth Automata and Bounded Treewidth Courcelle's Theorem More on Width-Metrics: Applications and Local Treewidth Depth-First Search and the Plehn-Voigt Theorem Other Width Metrics Part IV: Exotic Meta-Techniques Well-Quasi-Orderings and the Robertson-Seymour Theorems The Graph Minor Theorem Applications of the Obstruction Principle and WQOs Part V: Hardness Theory Reductions The Basic Class W[1] and an Analog of Cook's Theorem Other Hardness Results The W-Hierarchy The Monotone and Antimonotone Collapses Beyond W-Hardness k-Move Games Provable Intractability: The Class XP Another Basis Part VI: Approximations, Connections, Lower Bounds The M-Hierarchy, and XP-optimality Kernelization Lower Bounds Part VII: Further Topics Parameterized Approximation Parameterized Counting and Randomization Part VIII: Research Horizons Research Horizons Part IX Appendices Appendix 1: Network Flows and Matchings Appendix 2: Menger's Theorems

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詳細情報

• NII書誌ID(NCID): BB14790219
• ISBN:
  • 9781447155584
  • 9781447171645
• LCCN: 2013955593
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: London
• ページ数/冊数: xxx, 763 p.
• 大きさ: 25 cm
• 件名:
  • LCSH : Computer algorithms
• 親書誌ID:
  • BA60860215