复杂性理论
2006-1
科学
韦格纳
308
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复杂性理论主要研究决定解决算法问题的必要资源，以及利用可用资源可能得到的结果的界，而对这些界的深入理解可以防止寻求不存在的所谓有效算法。复杂性理论的新分支随着新的算法概念而不断涌现，其产物——如NP一完备性理论——已经影响到计算机科学的所有领域的发展。本书视随机化为一个关键概念，强调理论与实际应用的相互作用。本书论题始终强调复杂性理论对于当今计算机科学的重要意义，包含各种具体应用。
1 Introduction 1.1 What Is Complexity Theory? 1.2 Didactic Background 1.3 Overview 1.4 Additional Literature2 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 Problems3 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 Randomization4 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 Reductions5 The Theory of NP-Completeness 5.1 Fundamental Considerations 5.2 Problems in NP 5.3 Alternative Characterizations of NP 5.4 Cook s Theorem6 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 Problems7 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 Considered8 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 Problems9 The Complexity of Black Box Problems 9.1 Black Box Optimization 9.2 Yao s Minimax Principle 9.3 Lower Bounds for Black Box COmplexity10 Additional Complexity Classes11 Interactive Proofs12 The PCP Theorem and the Complexity of Approximation Problems13 Further Topics From Classical Complexity Theory14 The Complexity of Non-uniform Problems15 Communication Complexity16 The Complexity of Boolean FunctionsFinal CommentsA Appendix A.1 Orders of Magnitude and O-Notation A.2 Results from Probability TheoryReferencesIndex
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内容不错不少新内容视角独特叙述也还行证明方面还是比较偏重想法