This is a graduate-level course in the design and analysis of algorithms. We study techniques for the design of algorithms (such as dynamic programming) and algorithms for fundamental problems (such as fast Fourier transform or FFT).
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In addition, we study computational intractability, specifically, the theory of NP-completeness. The main topics covered in the course include: dynamic programming; divide and conquer, including FFT; randomized algorithms, including RSA cryptosystem and hashing using Bloom filters; graph algorithms; max-flow algorithms; linear programming; and NP-completeness.
The design and analysis of algorithms form an essential basis for computer science. This course is useful for those who want to pursue advanced studies in computer science, as well as those who want to work as a software engineer.
What you will learn
Dynamic Programming
Fibonacci Numbers, Longest Increasing Subsequence (LIS), Longest Common Subsequence (LCS)
Knapsack, Chain Matrix Multiplication
Shortest Path Algorithms
Randomized Algorithms
Modular Arithmetic: Fast Modular Exponentiation, Multiplicative Inverses
RSA Cryptosystem: Fermat's Little Theorem, RSA Protocol, Primality Testing
Hashing: Traditional Chain Hashing, Bloom Filters
Divide and Conquer
Fast Integer Multiplication
Linear-Time Median
Fast Fourier Transform
Graph Algorithms
Strongly Connected Components, 2-Satisfiability
Minimum Spanning Tree
Markov Chains, PageRank
Max-Flow Problems
Ford-Fulkerson Algorithm
Max-Flow Min-Cut Theorem, Edmonds-Karp Algorithm
Max-Flow applied to Image Segmentation
Linear Programming
Simplex Algorithm
Weak and Strong Duality
Max-SAT Approximation
NP-Completeness
Complexity Classes: P, NP, NP-Complete
NP-Complete Problems: 3-SAT, Independent Set, Clique, Vertex Cover, Knapsack, Subset-Sum
Halting Problem
Prerequisites and requirements
Students are expected to have an undergraduate course on the design and analysis of algorithms. In particular, they should be familiar with basic graph algorithms, including DFS, BFS, and Dijkstra's shortest path algorithm, and basic dynamic programming and divide and conquer algorithms (including solving recurrences). An undergraduate course in discrete mathematics is assumed, and students should be comfortable analyzing the asymptotic running time of algorithms.
The course uses the textbook Algorithms by Sanjoy Dasgupta, Christos Papadimitriou, and Umesh Vazirani.
