| 1 Introduction 1.1 What Is Complexity Theory? 1.2 Didactic Background 1.3 Overview 1.4 Additional Literature 2 Algorithmic Problems & Their Complexity 2.1 What Are Algorithmic Problems? 2.2 Some Important Algorithmic Problems 2.3 Measuring Computation Time 2.4 The Complexity of Algorithmic Problems 3 Fundamental Complexity Classes 3.1 The Special Role of Polynomial Computation Time 3.2 Randomized Agorithms 3.3 The Fundamental Complexity Classes for Algorithmic Problems 3.4 The Fundamental Complexity Classes for Decision Problems 3.5 Nondeterminism as a Special Case of Randomization 4 Reductions-Algorithmic Relationships Between Problems 4.1 When Are Two Problems Algorithmically Similar? 4.2 Reductions Between Various Vaariants of a Problem 4.3 Reductions Between Related Problems 4.4 Reductions Between Unrelated Problems 4.5 The Special Role of Polynomial Reductions 5 The Theory of NP-Completeness 5.1 Fundamental Considerations 5.2 Problems in NP 5.3 Alternative Characterizations of NP 5.4 Cook s Theorem 6 NP-complete and NP-equivalent Problems 6.1 Fundamental Considerations 6.2 Traveling Salesperson Problems 6.3 Knapsack Problems 6.4 Partitioning and Scheduling Problems 6.5 Clique Problems 6.6 Team Building Problems 6.7 Championship Problems 7 The Complexity Analysis of Problems 7.1 The dividing Line Between Easy and Hard 7.2 Pseudo-polynomial Algorithms and Strong NP-comleteness 7.3 An Overview of the NP-competeness Proofs Considered 8 The Complexity of Approximation Problems-Classical Results 8.1 Complexity Classes 8.2 Approximation Algorithms 8.3 The Gap Technique 8.4 Approximation-Preserving Reductions 8.5 Complete Approximation Problems 9 The Complexity of Black Box Problems 9.1 Black Box Optimization 9.2 Yao s Minimax Principle 9.3 Lower Bounds for Black Box COmplexity 10 Additional Complexity Classes 11 Interactive Proofs 12 The PCP Theorem and the Complexity of Approximation Problems 13 Further Topics From Classical Complexity Theory 14 The Complexity of Non-uniform Problems 15 Communication Complexity 16 The Complexity of Boolean Functions Final Comments A Appendix A.1 Orders of Magnitude and O-Notation A.2 Results from Probability Theory References Index |
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