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February 10, 2025
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Approximation algorithms, Part 2
This is the continuation of Approximation algorithms, Part 1. Here you will learn linear programming duality applied to the design of some approximation algorithms, and semidefinite programming applied to Maxcut. By taking the two parts of 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 second of a two-part course on Approximation Algorithms.
This module does not study any specific combinatorial optimization problem. Instead, it introduces a central feature of linear programming, duality.
9 videos11 readings8 assignments1 peer review
This module uses linear programming duality to design an algorithm for another basic problem, the Steiner forest problem.
8 videos9 readings8 assignments1 peer review
This module continues teaching algorithmic applications of linear programming duality by applying it to another basic problem, the facility location problem.
9 videos10 readings8 assignments1 peer review
We introduce a generalization of linear programming, semi-definite programming.This module uses semi-definite programming to design an approximation algorithm for another basic problem, the maximum cut problem.
11 videos12 readings9 assignments1 peer review
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.
École normale supérieure
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EIT Digital
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University of Colorado Boulder
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University of Colorado Boulder
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Reviewed on Oct 27, 2016
Demanding course with lots of great algorithm concepts based on Linear Programming.
Reviewed on Feb 15, 2017
Even better than the first! Very good classes (except for the two first of week 3 ...)
Reviewed on Mar 13, 2016
It is remarkable to note that Professor Claire Mathieu explains such a complex subject in such a elegant and understandable manner.
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