Approximation Algorithms Part II
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Approximation Algorithms Part II at Coursera Overview
Duration | 33 hours |
Start from | Start Now |
Total fee | Free |
Mode of learning | Online |
Schedule type | Self paced |
Official Website | Explore Free Course  |
Credential | Certificate |
Approximation Algorithms Part II at Coursera Highlights
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- Approx. 33 hours to complete
- English Subtitles: French, Portuguese (European), Russian, English, Spanish
Approximation Algorithms Part II at Coursera Course details
- 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.
Approximation Algorithms Part II at Coursera Curriculum
Linear Programming Duality
Linear programming duality - example
Properties of LP duality
Geometry of LP duality
Proof of weak duality theorem
Changing the form of the LP
Complementary slackness
Primal-dual algorithms
Vertex cover by primal-dual
Conclusion
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Steiner Forest and Primal-Dual Approximation Algorithms
Problem definition
A special case: Steiner tree
LP relaxation for Steiner forest
... and its dual
Primal-dual algorithm, Part1
Primal-dual algorithm,Part 2
Analysis
Proof of the main lemma
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Facility Location and Primal-Dual Approximation Algorithms
Problem definition
A linear programming relaxation
...and its dual
A primal-dual algorithm
Analyzing the service cost
Analyzing the facility opening cost
A better algorithm
Analysis
Conclusion
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Maximum Cut and Semi-Definite Programming
Definition
A 2-approximation
A linear programming relaxation...
...with an integrality gap of almost 2
Proof of Lemma
A quadratic programming relaxation
General facts about semidefinite programming
A rounding algorithm
Analysis
General facts about MaxCut
The end!
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