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

美國康乃爾大學計算機繫教授Jon Kleinberg和éva Tardos合著的《算法設計》是近幾年當中關於算法設計和分析的不可多得的優秀教材。它適用於本科高年級學生以及研究生的算法課。它還很適於具有計算機或相近專業本科水平的人自學算法的需要。

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                                       ——黃連生  清華大學計算機繫

“Algorithm Design”是我看到過的關於算法設計好的教材之一。

                                        ——屈婉玲  北京大學信息學院

算法設計一書的前8章以及後面若干章節，構成本科生算法設計導論課程的基礎。後續的章節適合於更高級研究。本書包含200多道有趣簡明的作業問題?其中一些問題直接來自諸如Yahoo!和Oracle這樣的公司。每個問題都經過測試，表明這些問題的有效性和精確性。

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本書的特色在於努力剖析問題本質，分析較透徹，詳盡地分析了問題描述的方式，針對問題在不同情況下的求解方式進行深入的闡述。

                                           ——宋友  北京航空航天大學軟件學院

本書通過實際問題的求解過程來引入算法設計思想和分析方法，對每種技術選擇了多個典型範例進行分析，使讀者更深入地掌握算法設計的理論和技巧，是一本難得的算法教材。

                                         ——林永鋼  北京理工大學計算機學院