18.409 | Spring 2002 | Graduate
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
Course Info
Departments
As Taught In
Spring 2002
Level