Free Course

Introduction to Graduate Algorithms

Offered at Georgia Tech as CS 8803 GA

About this Course

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).

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.

Course Cost

Free

Timeline

Approx. 3 months

Skill Level

Advanced

Included in Course

Rich Learning Content
Interactive Quizzes
Taught by Industry Pros
Self-Paced Learning
Student Support Community

Course Leads

Eric Vigoda

Instructor
Arpan Chakraborty

Instructor

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.

See the Technology Requirements for using Udacity.

Why Take This Course

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 do I get?

Instructor videos
Learn by doing exercises
Taught by industry professionals

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