Computational Geometry

Course Outline

• Core Concepts
  • Convex Hulls
  • Voronoi Diagrams
  • Delaunay Triangulations
  • Arrangements and Duality
• Data Structures
  • Quad Trees and Range Trees
  • k-D trees
• Optimization
  • Polyhedra
  • Linear Programming
  • The Simplex and Ellipsoid methods
  • Semidefinite Programming
  • Parametric search/Randomization
  • Net-and-prune
• Range Spaces
  • VC-dimension and friends
  • eps-nets and samples
  • Cuttings and Partition Trees
• High Dimensional Geometry
  • Random Projections and SVDs
  • Near Neighbours and LSH
  • Core Sets
• The Geometry of Machine Learning
  • Kernels and SVMs
  • Graph Laplacians
  • Information Geometry

Course Mechanics

• Homeworks: 80%
• Project: 20%