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Last updated:

September 23, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

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, condition numbers/parametric analysis, and subclassing inputs.

Course Curriculum

  • The Condition Number Unlimited
  • The Largest Singular Value of a Matrix Unlimited
  • Gaussian Elimination Without Pivoting Unlimited
  • Smoothed Analysis of Gaussian Elimination Without Pivoting Unlimited
  • Growth Factors of Partial and Complete Pivoting Unlimited
  • Spectral Partitioning Introduced Unlimited
  • Spectral Partitioning of Planar Graphs Unlimited
  • Spectral Parititioning of Well-Shaped Meshes and Nearest Neighbor Graphs Unlimited
  • Smoothed Analysis and Monotone Adversaries for Bandwidth and Graph Bisection Unlimited
  • Introduction to Linear Programming Unlimited
  • Strong Duality Theorem of Linear Programming Unlimited
  • Analysis of von Neumann’s Algorithm Unlimited
  • Worst-Case Complexity of the Simplex Method Unlimited
  • The Expected Number of Unlimited
  • The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane (cont.) Unlimited
  • The Expected Number of Facets of the Shadow of a Polytope Given by Gaussian Random Constraints Unlimited
  • The Expected Number of Facets of the Shadow of a Polytope Given by Gaussian Random Constraints: Angle Bound and Overview of Phase 1 Unlimited

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Massachusetts Institute of Technology
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