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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