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This course is a study of Behavior of Algorithms and covers an area of current interest in theoretical computer science. The topics vary from term to term. During this term, we discuss rigorous approaches to explaining the typical performance of algorithms with a focus on the following approaches smoothed analysis. In addition to that, condition numbers/parametric analysis, and subclassing inputs will be discussed.  

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: MIT

Course Curriculum

The Condition Number 00:05:00
The Largest Singular Value of a Matrix 00:05:00
Gaussian Elimination Without Pivoting 00:10:00
Smoothed Analysis of Gaussian Elimination Without Pivoting 00:05:00
Growth Factors of Partial and Complete Pivoting 00:10:00
Spectral Partitioning Introduced 00:05:00
Spectral Partitioning of Planar Graphs 00:05:00
Spectral Parititioning of Well-Shaped Meshes and Nearest Neighbor Graphs 00:05:00
Smoothed Analysis and Monotone Adversaries for Bandwidth and Graph Bisection 00:05:00
Introduction to Linear Programming 00:05:00
Strong Duality Theorem of Linear Programming 00:10:00
Analysis of von Neumann’s Algorithm 00:10:00
Worst-Case Complexity of the Simplex Method 00:05:00
The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane – Part I 00:05:00
The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane – Part II 00:05:00
The Expected Number of Facets of the Shadow of a Polytope Given by Gaussian Random Constraints – Part I 00:05:00
The Expected Number of Facets of the Shadow of a Polytope Given by Gaussian Random Constraints – Part II 00:10:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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