#### 100% online

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

#### Approx. 12 hours to complete

Suggested: 9 hours/week...

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

#### Approx. 12 hours to complete

Suggested: 9 hours/week...

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
1 hour to complete

## Introduction to Approximation algorithms

In the module the motivation for studying approximation algorithms will be given. We will discuss what optimization problems are, and what the difference between heuristics and approximation algorithms is. Finally, we will introduce the concept of approximation ratio, which plays a central role in the analysis of the quality of approximation algorithms....
1 video (Total 13 min), 1 reading, 1 quiz
1 video
Course notes 1.130m
1 practice exercise
Introduction20m
Week
2
5 hours to complete

## The Load Balancing problem

In this module we will study various approximation algorithms for the load balancing problem. This problems asks to distribute a given set of jobs, each with a certain processing time, over a number of machine. The goal is to do this such that all jobs are finished as soon as possible. We will analyze the quality of the computed solutions computed using the concept of rho-approximation, which we saw in the previous lecture. In this analysis we will see that lower bounds on the optimal solution play a crucial role in the analysis (or, for maximization problems: upper bounds)....
3 videos (Total 45 min), 1 reading, 2 quizzes
3 videos
Analysis of the greedy-algorithm19m
The ordered scheduling algorithm14m
Course notes 1.245m
1 practice exercise
The load balancing problem25m
Week
3
3 hours to complete

## LP Relaxation

In this module we will introduce the technique of LP relaxation to design approximation algorithms, and explain how to analyze the approximation ratio of an algorithm based in LP relaxation. We will do this using the (weighted) Vertex Cover problem as an example. Before we explain the technique of LP relaxation, however, we first give a simple 2-approximation algorithm for the unweighted Vertex Cover problem. ...
6 videos (Total 69 min), 2 readings, 1 quiz
6 videos
An approximation algorithm for vertex-cover11m
A brief introduction to linear programming12m
Weighted vertex-cover15m
LP relaxation for weighted vertex-cover7m
LP relaxation: Analyzing approximation ratio12m
Course notes 3.120m
Course notes 3.245m
1 practice exercise
LP Relaxation30m
Week
4
6 hours to complete

## Polynomial-time approximation schemes

In this module we will introduce the concept of Polynomial-Time Approximation Scheme (PTAS), which are algorithms that can get arbitrarily close to an optimal solution. We describe a general technique to design PTASs, and apply it to the famous Knapsack problem. Finally we will see how to analyze PTASs that are designed with the general technique....
6 videos (Total 62 min), 2 readings, 2 quizzes
6 videos
Knapsack Problem6m
A dynamic-programming algorithm for knapsack16m
A PTAS for knapsack12m
Analysis of the PTAS for knapsack: approximation ratio11m
Analysis of the PTAS for knapsack: running time8m
Course notes 4.145m
Course notes 4.245m
1 practice exercise
Polynomial-time approximation schemes45m

## Instructor

### Mark de Berg

Prof.dr.
Mathematics and Computer Science

## About EIT Digital

EIT Digital is a pan-European education and research-based open innovation organization founded on excellence. Its mission is to foster digital technology innovation and entrepreneurial talent for economic growth and quality of life. By linking education, research and business, EIT Digital empowers digital top talents for the future. EIT Digital provides online "blended" Innovation and Entrepreneurship education to raise quality, increase diversity and availability of the top-level content provided by 20 reputable universities of technology around Europe. The universities all together deliver a unique blend of the best of technical excellence and entrepreneurial skills and mindset to digital engineers and entrepreneurs at all stages of their careers. The academic partners support Coursera’s bold vision to enable anyone, anywhere, to transform their lives by accessing the world’s best learning experience. This means that EIT Digital gradually shares parts of its entrepreneurial and academic education programmes to demonstrate its excellence and make it accessible to a much wider audience. EIT Digital’s online education portfolio can be used as part of blended education settings, in both Master and Doctorate programmes, and for professionals as a way to update their knowledge. EIT Digital offers an online programme in 'Internet of Things through Embedded Systems'. Achieving all certificates of the online courses and the specialization provides an opportunity to enroll in the on campus program and get a double degree. These are the courses in the online programme: ...

## Frequently Asked Questions

• Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.