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Parameterized Complexity Rodney G. Downey

Parameterized Complexity By Rodney G. Downey

Parameterized Complexity by Rodney G. Downey

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Summary

An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability. The authors consider the problem in terms of parameterized languages and taking k-slices of the language, thus introducing readers to new classes of algorithms which may be analysed more precisely than was the case until now.

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Parameterized Complexity Summary

Parameterized Complexity by Rodney G. Downey

An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability. The authors consider the problem in terms of parameterized languages and taking k-slices of the language, thus introducing readers to new classes of algorithms which may be analysed more precisely than was the case until now. The book is as self-contained as possible and includes a great deal of background material. As a result, computer scientists, mathematicians, and graduate students interested in the design and analysis of algorithms will find much of interest.

Table of Contents

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.- 2.1 Fixed-Parameter Tractability.- 2.2 The Advice View.- 3 Some Ad Hoc Methods: The Methods of Bounded Search Tree and Problem Kernel.- 3.1 The Method of Bounded Search Trees.- 3.1.1 The Basic Method.- 3.1.2 Heuristic Improvements, Shrinking the Search Tree.- 3.2 The Method of Reduction to a Problem Kernel.- 3.2.1 The Basic Method.- 3.2.2 Hereditary Properties and Leizhen Cai's Theorem.- 4 Optimization Problems, Approximation Schemes, and Their Relation with FPT.- 4.1 Optimization Problems.- 4.2 How FPT and Optimization Problems Relate.- 4.3 The Classes MAXSNP, MIN F+?1(h), and FPT.- 5 The Advice View Revisited and LOGSPACE.- 6 Methods via Automata and Bounded Treewidth.- 6.1 Classical Automata Theory.- 6.1.1 Deterministic Finite Automata.- 6.1.2 Nondeterministic Finite Automata.- 6.1.3 Regular Languages.- 6.1.4 The Myhill-Nerode Theorem and the Method of Test Sets.- 6.1.5 Classical Tree Automata.- 6.2 Treewidth.- 6.3 Bodlaender's Theorem.- 6.4 Parse Trees for Graphs of Bounded Treewidth and an Analog of the Myhill-Nerode Theorem.- 6.5 Courcelle's Theorem.- 6.5.1 The Basic Theorem.- 6.5.2 Implementing Courcelle's Theorem.- 6.6 Seese's Theorem.- 6.7 Notes on MS1 Theory.- 7 Well-Quasi-Orderings and the Robertson-Seymour Theorems.- 7.1 Basic WQO Theory.- 7.2 Thomas' Lemma.- 7.2.1 Thomas' Lemma Fails for Path Decompositions.- 7.3 The Graph Minor Theorem for Bounded Treewidth.- 7.4 Excluding a Forest.- 7.5 Connections with Automata Theory and Boundaried Graphs.- 7.6 A Sketch of the Proof of the Graph Minor Theorem.- 7.7 Immersions and the Nash-Williams Conjecture.- 7.8 Applications of the Obstruction Principle and WQO's.- 7.9 Effectivizations of Obstruction-Based Methods.- 7.9.1 Effectivization by Self-Reduction.- 7.9.2 Effectivization by Obstruction Set Computation.- 8 Miscellaneous Techniques.- 8.1 Depth-First Search.- 8.2 Bounded-Width Subgraphs, the Plehn-Voigt Theorem, and Induced Subgraphs.- 8.3 Hashing.- II Parameterized Intractability.- 9 Reductions.- 10 The Basic Class W[1] and an Analog of Cook's 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.- 17.1 Classical Complexity.- 17.2 Nondeterminism in P, LOGNP, and the Cai-Chen Model and Other Models.- 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.- 19.1 Some Tools.- 19.2 Results.- 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 Connections Between Classical and Parameterized Complexity.- B.4 Classification Gaps.- B.5 Structural Issues and Analogs of Classical Results.- References.

Additional information

CIN038794883XG
9780387948836
038794883X
Parameterized Complexity by Rodney G. Downey
Rodney G. Downey
Monographs in Computer Science
Used - Good
Hardback
Springer-Verlag New York Inc.
19981106
533
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us

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