大学算法设计与分析

课程介绍
       本课程系统介绍算法设计与分析的方法和理论,包括算法基础、图、贪婪算法、分治、动态规划、网络流、计算复杂性初步、近似算法及随机算法等。同时,本课程还包含算法领域的一些前沿课题和最新进展。本课程可以作为数学、计算机等相关专业的研究生和高年级本科生关于算法理论的基础课程。

课程章节
1 Introduction of Algorithm
1.1 Introduction
1.2 A First Problem: Stable Matching
1.3 Gale-Shapley Algorithm
1.4 Understanding Gale-Shapley Algorithm

2 Basics of Algorithm Analysis 
2.1 Computational Tractability
2.2 Asymptotic Order of Growth
2.3 A Survey of Common Running Times

3 Graph 
3.1 Basic Definitions and Applications
3.2 Graph Traversal
3.3 Testing Bipartiteness
3.4 Connectivity in Directed Graphs
3.5 DAG and Topological Ordering

4 Greedy Algorithms 
4.1 Coin Changing
4.2 Interval Scheduling
4.3 Interval Partitioning
4.4 Scheduling to Minimize Lateness
4.5 Optimal Caching
4.6 Shortest Paths in a Graph
4.7 Minimum Spanning Tree
4.8 Correctness of Algorithms
4.9 Clustering

5 Divide and Conquer 
5.1 Mergesort
5.2 Counting Inversions
5.3 Closest Pair of Points
5.4 Integer Multiplication
5.5 Matrix Multiplication
5.6 Convolution and FFT
5.7 FFT
5.8 Inverse DFT

6 Dynamic Programming 
6.1 Weighted Interval Scheduling
6.2 Segmented Least Squares
6.3 Knapsack Problem
6.4 RNA Secondary Structure
6.5 Sequence Alignment
6.6 Shortest Paths

7 Network Flow 
7.1 Flows and Cuts
7.2 Minimum Cut and Maximum Flow
7.3 Ford-Fulkerson Algorithm
7.4 Choosing Good Augmenting Paths
7.5 Bipartite Matching

8 NP and Computational Intractability 
8.1 Polynomial-Time Reductions
8.2 Basic Reduction Strategies I
8.3 Basic Reduction Strategies II
8.4 Definition of NP
8.5 Problems in NP
8.6 NP-Completeness
8.7 Sequencing Problems
8.8 Numerical Problems
8.9 co-NP and the Asymmetry of NP

9 Approximation Algorithms 
9.1 Load Balancing
9.2 Center Selection
9.3 The Pricing Method: Vertex Cover
9.4 LP Rounding: Vertex Cover
9.5 Knapsack Problem

10 Local Search 
10.1 Landscape of an Optimization Problem
10.2 Maximum Cut
10.3 Nash Equilibria
10.4 Price of Stability

11 Randomized Algorithms 
11.1 Contention Resolution
11.2 Linearity of Expectation
11.3 MAX 3-SAT
11.4 Chernoff Bounds

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