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Georgia Institute of Technology

Introduction to Graduate Algorithms

Georgia Institute of Technology via Udacity

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Overview

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.

Syllabus

  • 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

Taught by

Arpan Chakraborty and Eric Vigoda

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Reviews

5.0 rating, based on 1 Class Central review

Start your review of Introduction to Graduate Algorithms

  • Profile image for Tanisha Patil
    Tanisha Patil
    these introduction is helpful it develop the my knowledge also develop basic knowledge intoduction is is introduce about the advanced algorithm...its easy to solve the problems releted to the advanced algorithm it explain in detailed
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