Behavior of Algorithms

Calendar

LEC #	TOPICS
1	Introduction
2	The Condition Number
3	The Largest Singular Value of a Matrix
4	Gaussian Elimination without Pivoting
5	Smoothed Analysis of Gaussian Elimination without Pivoting
6	Growth Factors of Partial and Complete Pivoting Speeding up GE of Graphs with Low Bandwidth or Small Separators
7	Spectral Partitioning Introduced
8	Spectral Partitioning of Planar Graphs
9	Spectral Paritioning of Well-Shaped Meshes and Nearest Neighbor Graphs Turner’s Theorem for Bandwidth of Semi-Random Graphs
10	Smoothed Analysis and Monotone Adversaries for Bandwidth and Graph Bisection McSherry’s Spectral Bisection Algorithm
11	Introduction to Linear Programming von Neumann’s Algorithm, Primal and Dual Simplex Methods Duality
12	Strong Duality Theorem of Linear Programming Renegar’s Condition Numbers
13	Analysis of von Neumann’s Algorithm
14	Worst-Case Complexity of the Simplex Method
15	The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane
16	The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane (cont.)
17	The Expected Number of Facets of the Shadow of a Polytope given by Gaussian Random Constraints
18	The Expected Number of Facets of the Shadow of a Polytope given by Gaussian Random Constraints: Distance Bound
19	The Expected Number of Facets of the Shadow of a Polytope given by Gaussian Random Constraints: Angle Bound and Overview of Phase 1