Approximation Algorithms Part II
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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.

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课程大纲

  • Week 1 - Linear Programming Duality
    This module does not study any specific combinatorial optimization problem. Instead, it introduces a central feature of linear programming, duality.
  • Week 2 - Steiner Forest and Primal-Dual Approximation Algorithms
    This module uses linear programming duality to design an algorithm for another basic problem, the Steiner forest problem.
  • Week 3 - Facility Location and Primal-Dual Approximation Algorithms
    This module continues teaching algorithmic applications of linear programming duality by applying it to another basic problem, the facility location problem.
  • Week 4 - Maximum Cut and Semi-Definite Programming
    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.
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教师

Claire Mathieu

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École normale supérieure

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.

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Coursera

Coursera是一家数字公司,提供由位于加利福尼亚州山景城的计算机教师Andrew Ng和达芙妮科勒斯坦福大学创建的大型开放式在线课程。

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