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Approximation Algorithms

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Course Summary

Learn how to design approximation algorithms and analyze them with the Approximation Algorithms course on Coursera.

Key Learning Points

Understand the basics of approximation algorithms and their application in real-world problems
Learn how to design approximation algorithms and analyze their performance
Explore various techniques used in approximation algorithms, such as linear programming and randomized rounding

Learning Outcomes

Ability to design approximation algorithms for real-world problems
Understanding of techniques used in approximation algorithms
Ability to analyze the performance of approximation algorithms

Prerequisites or good to have knowledge before taking this course

Basic knowledge of algorithms and data structures
Familiarity with mathematical concepts such as calculus and probability theory

Course Difficulty Level

Intermediate

Course Format

Online Self-paced
Video Lectures
Quizzes and Assignments

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Description

Many real-world algorithmic problems cannot be solved efficiently using traditional algorithmic tools, for example because the problems are NP-hard. The goal of this course is to become familiar with important algorithmic concepts and techniques needed to effectively deal with such problems. These techniques apply when we don't require the optimal solution to certain problems, but an approximation that is close to the optimal solution. We will see how to efficiently find such approximations.

Prerequisites: In order to successfully take this course, you should already have a basic knowledge of algorithms and mathematics. Here's a short list of what you are supposed to know: - O-notation, Ω-notation, Θ-notation; how to analyze algorithms - Basic calculus: manipulating summations, solving recurrences, working with logarithms, etc. - Basic probability theory: events, probability distributions, random variables, expected values etc. - Basic data structures: linked lists, stacks, queues, heaps - (Balanced) binary search trees - Basic sorting algorithms, for example MergeSort, InsertionSort, QuickSort - Graph terminology, representations of graphs (adjacency lists and adjacency matrix), basic graph algorithms (BFS, DFS, topological sort, shortest paths) The material for this course is based on the course notes that can be found under the resources tab. We will not cover everything from the course notes. The course notes are there both for students who did not fully understand the lectures as well as for students who would like to dive deeper into the topics. The video lectures contain a few very minor mistakes. A list of these mistakes can be found under resources (in the document called "Errata"). If you think you found an error, report a problem by clicking the square flag at the bottom of the lecture or quiz where you found the error.

Outline

Introduction to Approximation algorithms
Introduction to Approximation Algorithms
Course notes 1.1
Introduction

The Load Balancing problem
A greedy algorithm for load balancing
Analysis of the greedy-algorithm
The ordered scheduling algorithm
Course notes 1.2
The load balancing problem

LP Relaxation
The vertex-cover problem
An approximation algorithm for vertex-cover
A brief introduction to linear programming
Weighted vertex-cover
LP relaxation for weighted vertex-cover
LP relaxation: Analyzing approximation ratio
Course notes 3.1
Course notes 3.2
LP Relaxation

Polynomial-time approximation schemes
Polynomial-time approximation schemes
Knapsack Problem
A dynamic-programming algorithm for knapsack
A PTAS for knapsack
Analysis of the PTAS for knapsack: approximation ratio
Analysis of the PTAS for knapsack: running time
Course notes 4.1
Course notes 4.2
Polynomial-time approximation schemes

Summary of User Reviews

The Approximation Algorithms course on Coursera has received positive reviews from many users. The course covers a range of topics related to approximation algorithms and provides a comprehensive understanding of the subject. Users have praised the course for its informative content and engaging teaching style.

Key Aspect Users Liked About This Course

The course is well-structured and covers a variety of topics related to approximation algorithms.

Pros from User Reviews

The course provides a comprehensive understanding of approximation algorithms.
The content is informative and engaging.
The teaching style is clear and easy to follow.
The course is well-structured and covers a range of topics.
The course provides excellent resources for further study.

Cons from User Reviews

Some users found the course challenging.
The course requires a strong background in mathematics.
The course may not be suitable for beginners.
The course can be time-consuming.
Some users found the course to be too theoretical.

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