算法设计 英文版

这是一本关于算法设计和分析的教材。本书围绕算法设计进行组织，对每种算法技术选择了多个典型范例进行分析，把算法的理论跟实际存在的问题结合起来，具有很大的启发性。本书侧重算法设计思路，不再赘述算法复杂度的分析，每章都从实际问题出发，经过深入的具体分析引出相应的算法的设计思想，并对算法的正确性和复杂性进行合理的分析和论证。本书覆盖面很宽，且含有200多道精彩的习题，还扩展了PSPACE问题、参数复杂性等内容。

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

Jon Kleinberg是美国国家科学院（NAS）、美国国家工程院（NAE）、美国人文与科学院（AAAS）三料院士。在计算机科学领域是“传说级”的人物，而且还获得过国际数学家大会颁发“奈望林纳奖”，该奖是数学家大会为了表彰信息科学方面的重要数学贡献而设的。

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