What Does a Front-End Developer Do?
February 10, 2025
Article · 5 min read
(554 reviews)
(554 reviews)
34 assignments
Approximation algorithms, Part I
How efficiently can you pack objects into a minimum number of boxes? How well can you cluster nodes so as to cheaply separate a network into components around a few centers? These are examples of NP-hard combinatorial optimization problems. It is most likely impossible to solve such problems efficiently, so our aim is to give an approximate solution that can be computed in polynomial time and that at the same time has provable guarantees on its cost relative to the optimum. This course assumes knowledge of a standard undergraduate Algorithms course, and particularly emphasizes algorithms that can be designed using linear programming, a favorite and amazingly successful technique in this area. By taking this course, you will be exposed to a range of problems at the foundations of theoretical computer science, and to powerful design and analysis techniques. Upon completion, you will be able to recognize, when faced with a new combinatorial optimization problem, whether it is close to one of a few known basic problems, and will be able to design linear programming relaxations and use randomized rounding to attempt to solve your own problem. The course content and in particular the homework is of a theoretical nature without any programming assignments. This is the first of a two-part course on Approximation Algorithms.
We introduce the course topic by a typical example of a basic problem, called Vertex Cover, for which we will design and analyze a state-of-the-art approximation algorithm using two basic techniques, called Linear Programming Relaxation and Rounding. It is a simple, elementary application of powerful techniques.
8 videos13 readings7 assignments1 peer review
This module shows the power of rounding by using it to design a near-optimal solution to another basic problem: the Knapsack problem.
7 videos9 readings7 assignments1 peer review
This module shows the sophistication of rounding by using a clever variant for another basic problem: bin packing. (This is a more advanced module.)
8 videos10 readings7 assignments1 peer review
This module introduces a simple and powerful variant of rounding, based on probability: randomized rounding. Its power is applied to another basic problem, the Set Cover problem.
8 videos11 readings8 assignments1 peer review
This module deepens the understanding of randomized rounding by developing a sophisticated variant and applying it to another basic problem, the Multiway Cut problem. (This is a more advanced module.)
5 videos8 readings5 assignments1 peer review
We asked all learners to give feedback on our instructors based on the quality of their teaching style.
L’École normale supérieure (ENS) est un établissement d'enseignement supérieur pour les études prédoctorales et doctorales (graduate school) et un haut lieu de la recherche française. L'ENS offre à 300 nouveaux étudiants et 200 doctorants chaque année une formation de haut niveau, largement pluridisciplinaire, des humanités et sciences sociales aux sciences dures. Régulièrement distinguée au niveau international, l'ENS a formé 10 médailles Fields et 13 prix Nobel.
Microsoft
Course
Specialization
Hebrew University of Jerusalem
Course
554 reviews
75.99%
20.93%
2.16%
0.90%
0%
Showing 3 of 554
Reviewed on Jan 26, 2016
The course provides a high-level introduction to approximation algorithm. There is no programming assignments but it provides nice introduction to approximation algorithm.
Reviewed on Sep 16, 2017
This course is awesome. Prof. managed to elaborate the problem and analysis clearly and homework is properly assigned.
Reviewed on Jan 18, 2016
This course is quite advanced and the assignments require prerequisite skills to prove time complexity etc. If you are upto it, then for sure take this course. The instructor is quite thorough.
Unlimited access to 10,000+ world-class courses, hands-on projects, and job-ready certificate programs - all included in your subscription
Earn a degree from world-class universities - 100% online
Upskill your employees to excel in the digital economy
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.