算法设计 英文版

1　Introduction: Some Representative Problems / 引言：某些有代表性的问题　1
1.1　A First Problem: Stable Matching / 第 一个问题：稳定匹配　1
1.2　Five Representative Problems / 五个有代表性的问题　12
Solved　Exercises / 带解答的练习　19
Exercises　/ 练习　22
Notes　and Further Reading / 注释和进一步阅读　28
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1　Introduction: Some Representative Problems / 引言：某些有代表性的问题　1
1.1　A First Problem: Stable Matching / 第 一个问题：稳定匹配　1
1.2　Five Representative Problems / 五个有代表性的问题　12
Solved　Exercises / 带解答的练习　19
Exercises　/ 练习　22
Notes　and Further Reading / 注释和进一步阅读　28
2　Basics of Algorithm Analysis / 算法分析基础　29
2.1　Computational Tractability / 计算可解性　29
2.2　Asymptotic Order of Growth / 增长的渐近阶　35
2.3　Implementing the Stable Matching Algorithm Using Lists and Arrays / 用列表和数组实现稳定匹配算法42
2.4　A Survey of Common Running Times / 常用运行时间概述　47
2.5　A More Complex Data Structure: Priority Queues / 更复杂的数据结构：优先队列　57
Solved　Exercises / 带解答的练习　65
Exercises　/ 练习　67
Notes　and Further Reading / 注释和进一步阅读　70
3　Graphs / 图　73
3.1　Basic Definitions and Applications / 基本定义与应用　73
3.2　Graph Connectivity and Graph Traversal / 图的连通性与图的遍历　78
3.3　Implementing Graph Traversal Using Queues and Stacks / 用优先队列与栈实现图的遍历　87
3.4　Testing Bipartiteness: An Application of Breadth-First Search / 二分性测试：宽度优先搜索的应用　94
3.5　Connectivity in Directed Graphs / 有向图中的连通性　97
3.6　Directed Acyclic Graphs and Topological Ordering / 有向无环图与拓扑排序　99
Solved　Exercises / 带解答的练习　104
Exercises　/ 练习　107
Notes　and Further Reading / 注释和进一步阅读　112
4　Greedy Algorithms / 贪心算法　115
4.1　Interval Scheduling: The Greedy Algorithm Stays Ahead / 区间调度：贪心算法领先　116
4.2　Scheduling to Minimize Lateness: An Exchange Argument / 最小延迟调度：交换论证　125
4.3　Optimal Caching: A More Complex Exchange Argument / 最优高速缓存：更复杂的交换论证131
4.4　Shortest Paths in a Graph / 图的最短路径　137
4.5　The Minimum Spanning Tree Problem / 最小生成树问题　142
4.6　Implementing Kruskal’s Algorithm: The Union-Find Data Structure / 实现Kruskal算法：Union-Find数据结构　151
4.7　Clustering / 聚类　157
4.8　Huffman Codes and Data Compression / 赫夫曼码与数据压缩　161
4.9 Minimum-Cost Arborescences: A Multi-Phase Greedy Algorithm / 最小费用有向树：多阶段贪心算法　177
Solved　Exercises / 带解答的练习　183
Exercises　/ 练习　188
Notes　and Further Reading / 注释和进一步阅读　205
5　Divide and Conquer / 分治策略　209
5.1　A First Recurrence: The Mergesort Algorithm / 第 一个递推式：归并排序算法　210
5.2　Further Recurrence Relations / 更多的递推关系　214
5.3　Counting Inversions / 计数逆序　221
5.4　Finding the Closest Pair of Points / 找最接邻近的点对　225
5.5　Integer Multiplication / 整数乘法　231
5.6　Convolutions and the Fast Fourier Transform / 卷积与快速傅里叶变换　234
Solved　Exercises / 带解答的练习　242
Exercises　/ 练习　246
Notes　and Further Reading / 注释和进一步阅读　249
6　Dynamic Programming / 动态规划　251
6.1　Weighted Interval Scheduling: A Recursive Procedure / 带权的区间调度：递归过程　252
6.2　Principles of Dynamic Programming: Memoization or Iteration over Subproblems / 动态规划原理：备忘录或者子问题迭代　258
6.3　Segmented Least Squares: Multi-way Choices / 分段的最小二乘：多重选择　261
6.4　Subset Sums and Knapsacks: Adding a Variable / 子集和与背包：加一个变量　266
6.5　RNA Secondary Structure: Dynamic Programming over Intervals / RNA二级结构：在区间上的动态规划　272
6.6　Sequence Alignment / 序列比对　278
6.7　Sequence Alignment in Linear Space via Divide and Conquer / 通过分治策略在线性空间的序列比对　284
6.8　Shortest Paths in a Graph / 图中的最短路径　290
6.9　Shortest Paths and Distance Vector Protocols / 最短路径和距离向量协议　297
6.10 Negative Cycles in a Graph / 图中的负圈　301
Solved　Exercises / 带解答的练习　307
Exercises　/ 练习　312
Notes　and Further Reading / 注释和进一步阅读　335
7　Network Flow / 网络流　337
7.1　The Maximum-Flow Problem and the Ford-Fulkerson Algorithm / 最大流问题与Ford-Fulkerson算法　338
7.2　Maximum Flows and Minimum Cuts in a Network / 网络中的最大流与最小割　346
7.3　Choosing Good Augmenting Paths / 选择好的增广路径352
7.4 The Preflow-Push Maximum-Flow Algorithm / 前向流推动最大流算法　357
7.5　A First Application: The Bipartite Matching Problem / 第 一个应用：二分匹配问题　367
7.6　Disjoint Paths in Directed and Undirected Graphs / 有向与无向图中的不交路径　373
7.7　Extensions to the Maximum-Flow Problem / 对最大流问题的推广　378
7.8　Survey Design / 调查设计384
7.9　Airline Scheduling / 航线调度　387
7.10　Image Segmentation / 图像分割　391
7.11　Project Selection / 项目选择　396
7.12　Baseball Elimination / 棒球排除　400
7.13 A Further Direction: Adding Costs to the Matching Problem / 进一步的方向：对匹配问题增加费用　404
Solved　Exercises / 带解答的练习　411
Exercises　/ 练习　415
Notes　and Further Reading / 注释和进一步阅读　448
8　NP and Computational Intractability / NP与计算的难解性　451
8.1　Polynomial-Time Reductions / 多项式时间归约　452
8.2　Reductions via “Gadgets”: The Satisfiability Problem / 使用“零件”的归约：可满足性问题　459
8.3　Efficient Certification and the Definition of NP / 有效证书和NP的定义　463
8.4　NP-Complete Problems / NP完全问题　466
8.5　Sequencing Problems / 排序问题　473
8.6　Partitioning Problems / 划分问题　481
8.7　Graph Coloring / 图着色　485
8.8　Numerical Problems / 数值问题　490
8.9　Co-NP and the Asymmetry of NP / Co-NP及NP的不对称性　495
8.10　A Partial Taxonomy of Hard Problems / 难问题的部分分类　497
Solved　Exercises / 带解答的练习　500
Exercises　/ 练习　505
Notes　and Further Reading / 注释和进一步阅读　529
9　PSPACE: A Class of Problems beyond NP / PSPACE：一类超出NP的问题　531
9.1　PSPACE / PSPACE　531
9.2　Some Hard Problems in PSPACE / PSPACE中的难问题　533
9.3　Solving Quantified Problems and Games in Polynomial Space / 在多项式空间中解量化问题和博弈问题　536
9.4　Solving the Planning Problem in Polynomial Space / 在多项式空间内求解规划问题　538
9.5　Proving Problems PSPACE-Complete / 证明问题是PSPACE完全的　543
Solved　Exercises / 带解答的练习　547
Exercises　/ 练习　550
Notes　and Further Reading / 注释和进一步阅读　551
10　Extending the Limits of Tractability / 扩展易解性的界限　553
10.1　Finding Small Vertex Covers / 找小的顶点覆盖　554
10.2　Solving NP-Hard Problems on Trees / 在树上解NP难问题　558
10.3　Coloring a Set of Circular Arcs / 圆弧集着色　563
10.4 Tree Decompositions of Graphs / 图的树分解　572
10.5 Constructing a Tree Decomposition / 构造树分解　584
Solved　Exercises / 带解答的练习　591
Exercises　/ 练习　594
Notes　and Further Reading / 注释和进一步阅读　598
11　Approximation Algorithms / 近似算法　599
11.1　Greedy Algorithms and Bounds on the Optimum: A Load Balancing Problem / 贪心算法与最优值的界限：负载均衡问题　600
11.2　The Center Selection Problem / 中心选址问题　606
11.3　Set Cover: A General Greedy Heuristic / 集合覆盖：一般的贪心启发式方法　612
11.4　The Pricing Method: Vertex Cover / 定价法：顶点覆盖　618
11.5　Maximization via the Pricing Method: The Disjoint Paths Problem / 用定价法最大化：不交路径问题　624
11.6　Linear Programming and Rounding: An Application to Vertex Cover / 线性规划与舍入：对顶点覆盖的应用　630
11.7 Load Balancing Revisited: A More Advanced LP Application / 再论负载均衡：更高级的LP应用　637
11.8　Arbitrarily Good Approximations: The Knapsack Problem / 任意好的近似：背包问题　644
Solved　Exercises / 带解答的练习　649
Exercises　/ 练习　651
Notes　and Further Reading / 注释和进一步阅读　659
12　Local Search / 局部搜索　661
12.1　The Landscape of an Optimization Problem / 最优化问题的地形图　662
12.2　The Metropolis Algorithm and Simulated Annealing / Metropolis算法与模拟退火算法　666
12.3　An Application of Local Search to Hopfield Neural Networks / 局部搜索在Hopfield神经网络中的应用　671
12.4　Maximum-Cut Approximation via Local Search / 局部搜索对最大割近似的应用　676
12.5　Choosing a Neighbor Relation / 选择邻居关系　679
12.6 Classification via Local Search / 用局部搜索分类　681
12.7　Best-Response Dynamics and Nash Equilibria / 最佳响应动态过程与纳什均衡　690
Solved　Exercises / 带解答的练习　700
Exercises　/ 练习　702
Notes　and Further Reading / 注释和进一步阅读　705
13　Randomized Algorithms / 随机算法　707
13.1　A First Application: Contention Resolution / 第 一个应用：消除争用　708
13.2　Finding the Global Minimum Cut / 求完全最小割　714
13.3　Random Variables and Their Expectations / 随机变量及其期望　719
13.4　A Randomized Approximation Algorithm for MAX 3-SAT / 关于MAX 3-SAT的随机近似算法　724
13.5　Randomized Divide and Conquer: Median-Finding and Quicksort / 随机分治策略：求中位数与快速排序　727
13.6　Hashing: A Randomized Implementation of Dictionaries / 散列法：字典的随机实现　734
13.7　Finding the Closest Pair of Points: A Randomized Approach / 求最邻近点对：随机方法　741
13.8　Randomized Caching / 随机超高速缓存　750
13.9　Chernoff Bounds / 切尔诺夫界　758
13.10　Load Balancing / 负载均衡　760
13.11　Packet Routing / 包路由选择　762
13.12　Background: Some Basic Probability Definitions / 背景：某些基本概率定义　769
Solved　Exercises / 带解答的练习　776
Exercises　/ 练习　782
Notes　and Further Reading / 注释和进一步阅读　793
Epilogue:　Algorithms That Run Forever / 后记：永不停止运行的算法　795
References　/ 参考文献　805
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