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基于push-relabel方法解决maximum matching的算法
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基于push-relabel方法解决maximum matching的算法

Amber 大牛关于图论的总结 ,1.1M 大小.... 1. 图论 Graph Theory 1.1. 定义与术语 Definition and Glossary 1.1.1. 图与网络 Graph and Network 1.1.2. 图的术语 Glossary of Graph 1.1.3. 路径与回路 Path and Cycle 1.1.4. 连通性 Connectivity 1.1.5. 图论中特殊的集合 Sets in graph 1.1.6. 匹配 Matching 1.1.7. 树 Tree 1.1.8. 组合优化 Combinatorial optimization 1.2. 图的表示 Expressions of graph 1.2.1. 邻接矩阵 Adjacency matrix 1.2.2. 关联矩阵 Incidence matrix 1.2.3. 邻接表 Adjacency list 1.2.4. 弧表 Arc list 1.2.5. 星形表示 Star 1.3. 图的遍历 Traveling in graph 1.3.1. 深度优先搜索 Depth first search (DFS) 1.3.1.1. 概念 1.3.1.2. 求无向连通图中的桥 Finding bridges in undirected graph 1.3.2. 广度优先搜索 Breadth first search (BFS) 1.4. 拓扑排序 Topological sort 1.5. 路径与回路 Paths and circuits 1.5.1. 欧拉路径或回路 Eulerian path 1.5.1.1. 无向图 1.5.1.2. 有向图 1.5.1.3. 混合图 1.5.1.4. 无权图 Unweighted 1.5.1.5. 有权图 Weighed — 中国邮路问题The Chinese post problem 1.5.2. Hamiltonian Cycle 哈氏路径与回路 1.5.2.1. 无权图 Unweighted 1.5.2.2. 有权图 Weighed — 旅行商问题The travelling salesman problem 1.6. 网络优化 Network optimization 1.6.1. 最小生成树 Minimum spanning trees 1.6.1.1. 基本算法 Basic algorithms 1.6.1.1.1. Prim 1.6.1.1.2. Kruskal 1.6.1.1.3. Sollin（Boruvka） 1.6.1.2. 扩展模型 Extended models 1.6.1.2.1. 度限制生成树 Minimum degree-bounded spanning trees 1.6.1.2.2. k小生成树 The k minimum spanning tree problem(k-MST) 1.6.2. 最短路Shortest paths 1.6.2.1. 单源最短路 Single-source shortest paths 1.6.2.1.1. 基本算法 Basic algorithms 1.6.2.1.1.1. Dijkstra 1.6.2.1.1.2. Bellman-Ford 1.6.2.1.1.2.1. Shortest path faster algorithm(SPFA) 1.6.2.1.2. 应用Applications 1.6.2.1.2.1. 差分约束系统 System of difference constraints 1.6.2.1.2.2. 有向无环图上的最短路 Shortest paths in DAG 1.6.2.2. 所有顶点对间最短路 All-pairs shortest paths 1.6.2.2.1. 基本算法 Basic algorithms 1.6.2.2.1.1. Floyd-Warshall 1.6.2.2.1.2. Johnson 1.6.3. 网络流 Flow network 1.6.3.1. 最大流 Maximum flow 1.6.3.1.1. 基本算法 Basic algorithms 1.6.3.1.1.1. Ford-Fulkerson method 1.6.3.1.1.1.1. Edmonds-Karp algorithm 1.6.3.1.1.1.1.1. Minimum length path 1.6.3.1.1.1.1.2. Maximum capability path 1.6.3.1.1.2. 预流推进算法 Preflow push method 1.6.3.1.1.2.1. Push-relabel 1.6.3.1.1.2.2. Relabel-to-front 1.6.3.1.1.3. Dinic method 1.6.3.1.2. 扩展模型 Extended models 1.6.3.1.2.1. 有上下界的流问题 1.6.3.2. 最小费用流 Minimum cost flow 1.6.3.2.1. 找最小费用路 Finding minimum cost path 1.6.3.2.2. 找负权圈 Finding negative circle 1.6.3.2.3. 网络单纯形 Network simplex algorithm 1.6.4. 匹配 Matching 1.6.4.1. 二分图 Bipartite Graph 1.6.4.1.1. 无权图-匈牙利算法 Unweighted - Hopcroft and Karp algorithm 1.6.4.1.2. 带权图-KM算法 Weighted –Kuhn-Munkres(KM) algorithm 1.6.4.2. 一般图General Graph 1.6.4.2.1. 无权图-带花树算法 Unweighted - Blossom (Edmonds) 1.

amber大牛的图论总结 1. 图论 Graph Theory 1.1. 定义与术语 Definition and Glossary 1.1.1. 图与网络 Graph and Network 1.1.2. 图的术语 Glossary of Graph 1.1.3. 路径与回路 Path and Cycle 1.1.4. 连通性 Connectivity 1.1.5. 图论中特殊的集合 Sets in graph 1.1.6. 匹配 Matching 1.1.7. 树 Tree 1.1.8. 组合优化 Combinatorial optimization 1.2. 图的表示 Expressions of graph 1.2.1. 邻接矩阵 Adjacency matrix 1.2.2. 关联矩阵 Incidence matrix 1.2.3. 邻接表 Adjacency list 1.2.4. 弧表 Arc list 1.2.5. 星形表示 Star 1.3. 图的遍历 Traveling in graph 1.3.1. 深度优先搜索 Depth first search (DFS) 1.3.1.1. 概念 1.3.1.2. 求无向连通图中的桥 Finding bridges in undirected graph 1.3.2. 广度优先搜索 Breadth first search (BFS) 1.4. 拓扑排序 Topological sort 1.5. 路径与回路 Paths and circuits 1.5.1. 欧拉路径或回路 Eulerian path 1.5.1.1. 无向图 1.5.1.2. 有向图 1.5.1.3. 混合图 1.5.1.4. 无权图 Unweighted 1.5.1.5. 有权图 Weighed — 中国邮路问题The Chinese post problem 1.5.2. Hamiltonian Cycle 哈氏路径与回路 1.5.2.1. 无权图 Unweighted 1.5.2.2. 有权图 Weighed — 旅行商问题The travelling salesman problem 1.6. 网络优化 Network optimization 1.6.1. 最小生成树 Minimum spanning trees 1.6.1.1. 基本算法 Basic algorithms 1.6.1.1.1. Prim 1.6.1.1.2. Kruskal 1.6.1.1.3. Sollin（Boruvka） 1.6.1.2. 扩展模型 Extended models 1.6.1.2.1. 度限制生成树 Minimum degree-bounded spanning trees 1.6.1.2.2. k小生成树 The k minimum spanning tree problem(k-MST) 1.6.2. 最短路Shortest paths 1.6.2.1. 单源最短路 Single-source shortest paths 1.6.2.1.1. 基本算法 Basic algorithms 1.6.2.1.1.1. Dijkstra 1.6.2.1.1.2. Bellman-Ford 1.6.2.1.1.2.1. Shortest path faster algorithm(SPFA) 1.6.2.1.2. 应用Applications 1.6.2.1.2.1. 差分约束系统 System of difference constraints 1.6.2.1.2.2. 有向无环图上的最短路 Shortest paths in DAG 1.6.2.2. 所有顶点对间最短路 All-pairs shortest paths 1.6.2.2.1. 基本算法 Basic algorithms 1.6.2.2.1.1. Floyd-Warshall 1.6.2.2.1.2. Johnson 1.6.3. 网络流 Flow network 1.6.3.1. 最大流 Maximum flow 1.6.3.1.1. 基本算法 Basic algorithms 1.6.3.1.1.1. Ford-Fulkerson method 1.6.3.1.1.1.1. Edmonds-Karp algorithm 1.6.3.1.1.1.1.1. Minimum length path 1.6.3.1.1.1.1.2. Maximum capability path 1.6.3.1.1.2. 预流推进算法 Preflow push method 1.6.3.1.1.2.1. Push-relabel 1.6.3.1.1

中文名: 算法导论原名: Introduction to Algorithms 作者: Thomas H.Cormen, 达特茅斯学院计算机科学系副教授 Charles E.Leiserson, 麻省理工学院计算机科学与电气工程系教授 Ronald L.Rivest, 麻省理工学院计算机科学系Andrew与Erna Viterbi具名教授 Clifford Stein, 哥伦比亚大学工业工程与运筹学副教授资源格式: PDF（完整书签目录）出版社: The MIT Press ISBN 978-0-262-03384-8 (hardcover : alk. paper)—ISBN 978-0-262-53305-8 (pbk. : alk. paper) 发行时间: 2009年09月30日地区: 美国语言: 英文 1 The Role of Algorithms in Computing 5 1.1 Algorithms 5 1.2 Algorithms as a technology 11 2 Getting Started 16 2.1 Insertion sort 16 2.2 Analyzing algorithms 23 2.3 Designing algorithms 29 3 Growth of Functions 43 3.1 Asymptotic notation 43 3.2 Standard notations and common functions 53 4 Divide-and-Conquer 65 4.1 The maximum-subarray problem 68 4.2 Strassen's algorithm for matrix multiplication 75 4.3 The substitution method for solving recurrences 83 4.4 The recursion-tree method for solving recurrences 88 4.5 The master method for solving recurrences 93 4.6 Proof of the master theorem 97 5 Probabilistic Analysis and Randomized Algorithms 114 5.1 The hiring problem 114 5.2 Indicator random variables 118 5.3 Randomized algorithms 122 5.4 Probabilistic analysis and further uses of indicator random variables 130 II Sorting and Order Statistics Introduction 147 6 Heapsort 151 6.1 Heaps 151 6.2 Maintaining the heap property 154 6.3 Building a heap 156 6.4 The heapsort algorithm 159 6.5 Priority queues 162 7 Quicksort 170 7.1 Description of quicksort 170 7.2 Performance of quicksort 174 7.3 A randomized version of quicksort 179 7.4 Analysis of quicksort 180 8 Sorting in Linear Time 191 8.1 Lower bounds for sorting 191 8.2 Counting sort 194 8.3 Radix sort 197 8.4 Bucket sort 200 9 Medians and Order Statistics 213 9.1 Minimum and maximum 214 9.2 Selection in expected linear time 215 9.3 Selection in worst-case linear time 220 III Data Structures Introduction 229 10 Elementary Data Structures 232 10.1 Stacks and queues 232 10.2 Linked lists 236 10.3 Implementing pointers and objects 241 10.4 Representing rooted trees 246 11 Hash Tables 253 11.1 Direct-address tables 254 11.2 Hash tables 256 11.3 Hash functions 262 11.4 Open addressing 269 11.5 Perfect hashing 277 12 Binary Search Trees 286 12.1 What is a binary search tree? 286 12.2 Querying a binary search tree 289 12.3 Insertion and deletion 294 12.4 Randomly built binary search trees 299 13 Red-Black Trees 308 13.1 Properties of red-black trees 308 13.2 Rotations 312 13.3 Insertion 315 13.4 Deletion 323 14 Augmenting Data Structures 339 14.1 Dynamic order statistics 339 14.2 How to augment a data structure 345 14.3 Interval trees 348 IV Advanced Design and Analysis Techniques Introduction 357 15 Dynamic Programming 359 15.1 Rod cutting 360 15.2 Matrix-chain multiplication 370 15.3 Elements of dynamic programming 378 15.4 Longest common subsequence 390 15.5 Optimal binary search trees 397 16 Greedy Algorithms 414 16.1 An activity-selection problem 415 16.2 Elements of the greedy strategy 423 16.3 Huffman codes 428 16.4 Matroids and greedy methods 437 16.5 A task-scheduling problem as a matroid 443 17 Amortized Analysis 451 17.1 Aggregate analysis 452 17.2 The accounting method 456 17.3 The potential method 459 17.4 Dynamic tables 463 V Advanced Data Structures Introduction 481 18 B-Trees 484 18.1 Definition of B-trees 488 18.2 Basic operations on B-trees 491 18.3 Deleting a key from a B-tree 499 19 Fibonacci Heaps 505 19.1 Structure of Fibonacci heaps 507 19.2 Mergeable-heap operations 510 19.3 Decreasing a key and deleting a node 518 19.4 Bounding the maximum degree 523 20 van Emde Boas Trees 531 20.1 Preliminary approaches 532 20.2 A recursive structure 536 20.3 The van Emde Boas tree 545 21 Data Structures for Disjoint Sets 561 21.1 Disjoint-set operations 561 21.2 Linked-list representation of disjoint sets 564 21.3 Disjoint-set forests 568 21.4 Analysis of union by rank with path compression 573 VI Graph Algorithms Introduction 587 22 Elementary Graph Algorithms 589 22.1 Representations of graphs 589 22.2 Breadth-first search 594 22.3 Depth-first search 603 22.4 Topological sort 612 22.5 Strongly connected components 615 23 Minimum Spanning Trees 624 23.1 Growing a minimum spanning tree 625 23.2 The algorithms of Kruskal and Prim 631 24 Single-Source Shortest Paths 643 24.1 The Bellman-Ford algorithm 651 24.2 Single-source shortest paths in directed acyclic graphs 655 24.3 Dijkstra's algorithm 658 24.4 Difference constraints and shortest paths 664 24.5 Proofs of shortest-paths properties 671 25 All-Pairs Shortest Paths 684 25.1 Shortest paths and matrix multiplication 686 25.2 The Floyd-Warshall algorithm 693 25.3 Johnson's algorithm for sparse graphs 700 26 Maximum Flow 708 26.1 Flow networks 709 26.2 The Ford-Fulkerson method 714 26.3 Maximum bipartite matching 732 26.4 Push-relabel algorithms 736 26.5 The relabel-to-front algorithm 748 VII Selected Topics Introduction 769 27 Multithreaded Algorithms Sample Chapter - Download PDF (317 KB) 772 27.1 The basics of dynamic multithreading 774 27.2 Multithreaded matrix multiplication 792 27.3 Multithreaded merge sort 797 28 Matrix Operations 813 28.1 Solving systems of linear equations 813 28.2 Inverting matrices 827 28.3 Symmetric positive-definite matrices and least-squares approximation 832 29 Linear Programming 843 29.1 Standard and slack forms 850 29.2 Formulating problems as linear programs 859 29.3 The simplex algorithm 864 29.4 Duality 879 29.5 The initial basic feasible solution 886 30 Polynomials and the FFT 898 30.1 Representing polynomials 900 30.2 The DFT and FFT 906 30.3 Efficient FFT implementations 915 31 Number-Theoretic Algorithms 926 31.1 Elementary number-theoretic notions 927 31.2 Greatest common divisor 933 31.3 Modular arithmetic 939 31.4 Solving modular linear equations 946 31.5 The Chinese remainder theorem 950 31.6 Powers of an element 954 31.7 The RSA public-key cryptosystem 958 31.8 Primality testing 965 31.9 Integer factorization 975 32 String Matching 985 32.1 The naive string-matching algorithm 988 32.2 The Rabin-Karp algorithm 990 32.3 String matching with finite automata 995 32.4 The Knuth-Morris-Pratt algorithm 1002 33 Computational Geometry 1014 33.1 Line-segment properties 1015 33.2 Determining whether any pair of segments intersects 1021 33.3 Finding the convex hull 1029 33.4 Finding the closest pair of points 1039 34 NP-Completeness 1048 34.1 Polynomial time 1053 34.2 Polynomial-time verification 1061 34.3 NP-completeness and reducibility 1067 34.4 NP-completeness proofs 1078 34.5 NP-complete problems 1086 35 Approximation Algorithms 1106 35.1 The vertex-cover problem 1108 35.2 The traveling-salesman problem 1111 35.3 The set-covering problem 1117 35.4 Randomization and linear programming 1123 35.5 The subset-sum problem 1128 VIII Appendix: Mathematical Background Introduction 1143 A Summations 1145 A.1 Summation formulas and properties 1145 A.2 Bounding summations 1149 B Sets, Etc. 1158 B.1 Sets 1158 B.2 Relations 1163 B.3 Functions 1166 B.4 Graphs 1168 B.5 Trees 1173 C Counting and Probability 1183 C.1 Counting 1183 C.2 Probability 1189 C.3 Discrete random variables 1196 C.4 The geometric and binomial distributions 1201 C.5 The tails of the binomial distribution 1208 D Matrices 1217 D.1 Matrices and matrix operations 1217 D.2 Basic matrix properties 122

算法导论英文版，非图片版。 I Foundations Introduction 3 1 The Role of Algorithms in Computing 5 1.1 Algorithms 5 1.2 Algorithms as a technology 11 2 Getting Started 16 2.1 Insertion sort 16 2.2 Analyzing algorithms 23 2.3 Designing algorithms 29 3 Growth of Functions 43 3.1 Asymptotic notation 43 3.2 Standard notations and common functions 53 4 Divide-and-Conquer 65 4.1 The maximum-subarray problem 68 4.2 Strassen’s algorithm for matrix multiplication 75 4.3 The substitution method for solving recurrences 4.4 The recursion-tree method for solving recurrences 88 4.5 The master method for solving recurrences 93 ? 4.6 Proof of the master theorem 97 5 Probabilistic Analysis and Randomized Algorithms 114 5.1 The hiring problem 114 5.2 Indicator random variables 118 5.3 Randomized algorithms 122 ? 5.4 Probabilistic analysis and further uses of indicator random variables 130 83 vi Contents II Sorting and Order Statistics Introduction 147 6 Heapsort 151 6.1 Heaps 151 6.2 Maintaining the heap property 154 6.3 Building a heap 156 6.4 The heapsort algorithm 159 6.5 Priority queues 162 7 Quicksort 170 7.1 Description of quicksort 170 7.2 Performance of quicksort 174 7.3 A randomized version of quicksort 179 7.4 Analysis of quicksort 180 8 Sorting in Linear Time 191 8.1 Lower bounds for sorting 191 8.2 Counting sort 194 8.3 Radix sort 197 8.4 Bucket sort 200 9 Medians and Order Statistics 213 9.1 Minimum and maximum 214 9.2 Selection in expected linear time 215 9.3 Selection in worst-case linear time 220 III Data Structures Introduction 229 10 Elementary Data Structures 232 10.1 Stacks and queues 232 10.2 Linked lists 236 10.3 Implementing pointers and objects 241 10.4 Representing rooted trees 246 11 Hash Tables 253 11.1 Direct-address tables 254 11.2 Hash tables 256 11.3 Hash functions 262 11.4 Open addressing 269 ? 11.5 Perfect hashing 277 Contents vii 12 Binary Search Trees 286 12.1 What is a binary search tree? 286 12.2 Querying a binary search tree 289 12.3 Insertion and deletion 294 ? 12.4 Randomly built binary search trees 299 13 Red-Black Trees 308 13.1 Properties of red-black trees 308 13.2 Rotations 312 13.3 Insertion 315 13.4 Deletion 323 14 Augmenting Data Structures 339 14.1 Dynamic order statistics 339 14.2 How to augment a data structure 345 14.3 Interval trees 348 IV Advanced Design and Analysis Techniques Introduction 357 15 Dynamic Programming 359 15.1 Rod cutting 360 15.2 Matrix-chain multiplication 370 15.3 Elements of dynamic programming 378 15.4 Longest common subsequence 390 15.5 Optimal binary search trees 397 16 Greedy Algorithms 414 16.1 An activity-selection problem 16.2 Elements of the greedy strategy 423 16.3 Huffman codes 428 415 ? 16.4 Matroids and greedy methods 437 ? 16.5 A task-scheduling problem as a matroid 443 17 Amortized Analysis 451 17.1 Aggregate analysis 452 17.2 The accounting method 456 17.3 The potential method 459 17.4 Dynamic tables 463 viii Contents V Advanced Data Structures Introduction 481 18 B-Trees 484 18.1 Definition of B-trees 488 18.2 Basic operations on B-trees 491 18.3 Deleting a key from a B-tree 499 19 Fibonacci Heaps 505 19.1 Structure of Fibonacci heaps 507 19.2 Mergeable-heap operations 510 19.3 Decreasing a key and deleting a node 518 19.4 Bounding the maximum degree 523 20 van Emde Boas Trees 531 20.1 Preliminary approaches 532 20.2 A recursive structure 536 20.3 The van Emde Boas tree 545 21 Data Structures for Disjoint Sets 561 21.1 Disjoint-set operations 561 21.2 Linked-list representation of disjoint sets 564 21.3 Disjoint-set forests 568 ? 21.4 Analysis of union by rank with path compression 573 VI Graph Algorithms Introduction 587 22 Elementary Graph Algorithms 589 22.1 Representations of graphs 589 22.2 Breadth-first search 594 22.3 Depth-first search 22.4 Topological sort 612 22.5 Strongly connected components 615 23 Minimum Spanning Trees 624 23.1 Growing a minimum spanning tree 625 23.2 The algorithms of Kruskal and Prim 631 603 Contents ix 24 Single-Source Shortest Paths 643 24.1 The Bellman-Ford algorithm 651 24.2 Single-source shortest paths in directed acyclic graphs 24.3 Dijkstra’s algorithm 658 24.4 Difference constraints and shortest paths 664 24.5 Proofs of shortest-paths properties 671 655 25 All-Pairs Shortest Paths 684 25.1 Shortest paths and matrix multiplication 25.2 The Floyd-Warshall algorithm 693 25.3 Johnson’s algorithm for sparse graphs 686 700 26 Maximum Flow 708 26.1 Flow networks 709 26.2 The Ford-Fulkerson method 714 26.3 Maximum bipartite matching 732 ? 26.4 Push-relabel algorithms 736 ? 26.5 The relabel-to-front algorithm 748 VII Selected Topics Introduction 769 27 Multithreaded Algorithms 772 27.1 The basics of dynamic multithreading 27.2 Multithreaded matrix multiplication 792 27.3 Multithreaded merge sort 797 28 Matrix Operations 813 28.1 Solving systems of linear equations 813 28.2 Inverting matrices 827 28.3 Symmetric positive-definite matrices and least-squares approximation 832 29 Linear Programming 843 29.1 Standard and slack forms 850 29.2 Formulating problems as linear programs 859 29.3 The simplex algorithm 864 29.4 Duality 879 29.5 The initial basic feasible solution 886 774 x Contents 30 Polynomials and the FFT 898 30.1 Representing polynomials 900 30.2 The DFT and FFT 906 30.3 Efficient FFT implementations 915 31 Number-Theoretic Algorithms 926 31.1 Elementary number-theoretic notions 927 31.2 Greatest common divisor 933 31.3 Modular arithmetic 939 31.4 Solving modular linear equations 946 31.5 The Chinese remainder theorem 950 31.6 Powers of an element 954 31.7 The RSA public-key cryptosystem ? 31.8 Primality testing 965 ? 31.9 Integer factorization 975 958 32 String Matching 985 32.1 The naive string-matching algorithm 988 32.2 The Rabin-Karp algorithm 990 32.3 String matching with finite automata 995 ? 32.4 The Knuth-Morris-Pratt algorithm 1002 33 Computational Geometry 1014 33.1 Line-segment properties 1015 33.2 Determining whether any pair of segments intersects 1021 33.3 Finding the convex hull 1029 33.4 Finding the closest pair of points 1039 34 NP-Completeness 1048 34.1 Polynomial time 1053 34.2 Polynomial-time verification 1061 34.3 NP-completeness and reducibility 1067 34.4 NP-completeness proofs 1078 34.5 NP-complete problems 1086 35 Approximation Algorithms 1106 35.1 The vertex-cover problem 1108 35.2 The traveling-salesman problem 1111 35.3 The set-covering problem 1117 35.4 Randomization and linear programming 1123 35.5 The subset-sum problem 1128 Contents xi VIII Appendix: Mathematical Background Introduction 1143 A Summations 1145 A.1 Summation formulas and properties 1145 A.2 Bounding summations 1149 B Sets, Etc. 1158 B.1 Sets 1158 B.2 Relations 1163 B.3 Functions 1166 B.4 Graphs 1168 B.5 Trees 1173 C Counting and Probability 1183 C.1 Counting 1183 C.2 Probability 1189 C.3 Discrete random variables 1196 C.4 The geometric and binomial distributions 1201 D Matrices 1217 D.1 Matrices and matrix operations 1217 D.2 Basic matrix properties 1222 Bibliography 1231 Index 1251

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