算法设计

About the Authors Preface Introduction: Some Representative Problems 1.1 A First Problem: Stable Matching 1.2 Five Representative Problems Solved Exercises Exercises Notes and Further Reading Basics of Algorithm Ana/ys/s 2.1 Computational Tractability 2.2 Asymptotic Order of Growth 2.3 Implementing the Stable Matching Algorithm Using Lists and Arrays 2.4 A Survey of Common Running Times 2.5 A More Complex Data Structure: Priority Queues Solved Exercises Exercises Notes and Further Reading 3 Graphs 3.1 Basic Definitions and Applications 3.2 Graph Connectivity and Graph Traversal 3.3 Implementing Graph Traversal Using Queues and Stacks 3.4 Testing Bipaniteness: An Application of Breadth-First Search 3.5 Connectivity in Directed Graphs 3.6 Directed Acyclic Graphs and Topological Ordering Solved Exercises Exercises Notes and Further Reading 4 Greedy Algorithms 4.1 Interval Scheduling: The Greedy Algorithm Stays Ahead 4.2 Scheduling to Minimize Lateness: An Exchange Argument 4.3 Optimal Caching: A More Complex Exchange Argument 4.4 Shortest Paths in a Graph 4.5 The Minimum Spanning Tree Problem 4.6 Implementing Kruskal's Algorithm: The Union-Find Data Structure 4.7 Clustering 4.8 Huffman Codes and Data Compression * 4.9 Minimum-Cost Arborescences: A Multi-Phase Greedy Algorithm Solved Exercises Exercises Notes and Further Reading 5 D/v/de and Corn/net 5.1 A First Recurrence: The Mergesort Algorithm 5.2 Further Recurrence Relations 5.3 Counting Inversions 5.4 Finding the Closest Pair of Points 5.5 Integer Multiplication 5.6 Convolutions and the Fast Fourier Transform Solved Exercises Exercises Notes and Further Reading 6 Dynamic Programming 6.1 Weighted Interval Scheduling: A Recursive Procedure 6.2 Principles of Dynamic Programming: Memoization or Iteration over Subproblems 6.3 Segmented Least Squares: Multi-way Choices 6.4 Subset Sums and Knapsacks: Adding a Variable 6.5 RNA Secondary Structure: Dynamic Programming over Intervals 6.6 Sequence Alignment 6.7 Sequence Alignment in Linear Space via Divide and Conquer 6.8 Shortest Paths in a Graph 6.9 Shortest Paths and Distance Vector Protocols * 6.10 Negative Cycles in a Graph Solved Exercises Exercises Notes and Further Reading Network Flora 7.1 The Maximum-Flow Problem and the Ford-Fulkerson Algorithm 7.2 Maximum Flows and Minimum Cuts in a Network 7.3 Choosing Good Augmenting Paths * 7.4 The Preflow-Push Maximum-Flow Algorithm 7.5 A First Application: The Bipartite Matching Problem 7.6 Disjoint Paths in Directed and Undirected Graphs 7.7 Extensions to the Maximum-Flow Problem 7.8 Survey Design 7.9 Airline Scheduling 7.10 Image Segmentation 7.11 Project Selection 7.12 Baseball Elimination * 7.1.3 A Further Direction: Adding Costs to the Matching Problem Solved Exercises Exercises Notes and Further Reading NP and Computational Intractability 8.1 Polynomial-Time Reductions 8.2 Reductions via "Gadgets": The Safisfiability Problem 8.3 Efficient Certification and the Definition of NP 8.4 NP-Complete Problems 8.5 Sequencing Problems 8.6 Partitioning Problems 8.7 Graph Coloring 8.8 Numerical Problems 8.9 Co-NP and the Asymmetry of NP 8.10 A Partial Taxonomy of Hard Problems Solved Exercises Exercises Notes and Further Reading 9 PSPACE: A Class of Problems beyond NP 9.1 PSPACE 9.2 Some Hard Problems in PSPACE 9.3 Solving Quantified Problems and Games in Polynomial Space 9.4 Solving the Planning Problem in Polynomial Space 9.5 Proving Problems PSPACE-Complete Solved Exercises Exercises Notes and Further Reading 10 Extending the Limits of Tractability 10.1 Finding Small Vertex Covers 10.2 Solving NP-Hard Problems on Trees 10.3 Coloring a Set of Circular Arcs * 10.4 Tree Decompositions of Graphs * 10.5 Constructing a Tree Decomposition Solved Exercises Exercises Notes and Further Reading 11 Approximation Algorithms 11.1 Greedy Algorithms and Bounds on the Optimum: A Load Balancing Problem 11.2 The Center Selection Problem 11.3 Set Cover: A General Greedy Heuristic 11.4 The Pricing Method: Vertex Cover 11.5 Maximization via the Pricing Method: The Disjoint Paths Problem 11.6 Linear Programming and Rounding: An Application to Vertex Cover * 11.7 Load Balancing Revisited: A More Advanced LP Application 11.8 Arbitrarily Good Approximations: The Knapsack Problem Solved Exercises Exercises Notes and Further Reading Local Search 12.1 The Landscape of an Optimization Problem 12.2 The Metropolis Algorithm and Simulated Annealing 12.3 An Application of Local Search to Hopfield Neural Networks 12.4 Maximum-Cut Approximation via Local Search 12.5 Choosing a Neighbor Relation 12.6 Classification via Local Search 12.7 Best-Response Dynamics and Nash Equilibria Solved Exercises Exercises Notes and Further Reading Randomized Algorithms 13.1 A First Application: Contention Resolution 13.2 Finding the Global Minimum Cut 13.3 Random Variables and Their Expectations 13.4 A Randomized Approximation Algorithm for MAX 3-SAT 13.5 Randomized Divide and Conquer: Median-Finding and Quicksort 13.6 Hashing: A Randomized Implementation of Dictionaries 13.7 Finding the Closest Pair of Points: A Randomized Approach 13.8 Randomized Caching 13.9 Chernoff Bounds 13.10 Load Balancing 13.11 Packet Routing 13.12 Background: Some Basic Probability Definitions Solved Exercises Exercises Notes and Further Reading Epilogue: Algorithms That Run Forever References Index

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