
Limits to Parallel Computation
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Content
- Intro
- Contents
- Preface
- Part I: Background and Theory
- 1 Introduction
- 1.1 Bandersnatch Design
- 1.2 Informal Background
- 1.3 Some History
- 1.4 Related Works
- 1.5 Overview of This Book
- 2 Parallel Models of Computation
- 2.1 Introduction
- 2.2 The PRAM Model
- 2.3 The Boolean Circuit Model
- 2.4 Circuits and PRAMs
- 3 Complexity
- 3.1 Search and Decision Problems
- 3.2 Complexity Classes
- 3.3 Reducibility
- 3.4 Other NC Compatible Reducibilities
- 3.5 Completeness
- 4 Two Basic P-Complete Problems
- 4.1 The Generic P-Complete Problem
- 4.2 The Circuit Value Problem
- 5 Evidence That NC Does Not Equal P
- 5.1 Introduction
- 5.2 General Simulations Are Not Fast
- 5.3 Fast Simulations Are Not General
- 5.4 Natural Approaches Provably Fail
- 5.5 Summary
- 6 The Circuit Value Problem
- 6.1 The Circuit Value Problem Is P-Complete
- 6.2 Restricted Versions of Cimiit Value
- 7 Greedy Algorithms
- 7.1 Lexicographic Greedy Algorithms
- 7.2 Generic Greedy Algorithms
- 8 P-Complete Algorithms
- 8.1 Introduction
- 8.2 Inherently Sequential Algorithms
- 8.3 Applications of the Model
- 9 Two Other Notions of P-Completeness
- 9.1 Strong P-Completeness
- 9.2 Strict P-Completeness
- 10 Approximating P-Complete Problems
- 10.1 Introduction
- 10.2 Approximating LFMIS Is Hard
- 10.3 Approximation Schemes
- 11 Closing Remarks
- Part II: A Compendium of Problems
- A: P-Complete Problems
- A.1 Circuit Complexity
- A.2 Graph Theory
- A.3 Searching Graphs
- A.4 Combinatorial Optimization
- A.5 Local Optimality
- A.6 Logic
- A.7 Formal Languages
- A.8 Algebra
- A.9 Geometry
- A.10 Real Analysis
- A.11 Games
- A.12 Miscellaneous
- B: Open Problems
- B.1 Graph Theory
- B.2 Combinatorial Optimization
- B.3 Logic
- B.4 Formal Languages
- B.5 Algebra
- B.6 Geometry
- B.7 Real Analysis
- B.8 CC
- B.9 RNC
- C: Notation
- D: Complexity Classes
- D.1 Definitions
- D.2 Relationships Among Complexity Classes
- Bibliography
- Problem List
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- Y
- Z
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