Computational Geometry

  1. Advanced Topics
    1. Randomized Algorithms
      1. Randomized Incremental Construction
        1. General Framework
          1. Backward Analysis
            1. Expected Running Time
            2. Applications
              1. Convex Hulls
                1. Delaunay Triangulations
                  1. Linear Programming
                  2. Derandomization Techniques
                    1. Las Vegas vs Monte Carlo
                    2. Approximation Algorithms
                      1. Approximation Schemes
                        1. PTAS
                          1. FPTAS
                          2. Coresets
                            1. Construction Methods
                            2. Clustering Approximations
                              1. k-Means
                                1. k-Center
                                  1. Facility Location
                                2. High-Dimensional Geometry
                                  1. Curse of Dimensionality
                                    1. Volume Concentration
                                      1. Distance Concentration
                                        1. Nearest Neighbor Search
                                          1. kd-Tree Limitations
                                            1. Locality-Sensitive Hashing
                                              1. Random Projections
                                              2. Approximate Nearest Neighbor
                                                1. Algorithms
                                                  1. Trade-offs
                                                    1. Quality Measures
                                                  2. Topological Methods
                                                    1. Simplicial Complexes
                                                      1. Construction
                                                        1. Homology
                                                        2. Persistent Homology
                                                          1. Filtrations
                                                            1. Persistence Diagrams
                                                              1. Barcodes
                                                                1. Stability Theorems
                                                                2. Applications
                                                                  1. Shape Analysis
                                                                    1. Data Analysis
                                                                      1. Feature Detection
                                                                    2. Parallel and GPU Algorithms
                                                                      1. Parallel Computational Geometry
                                                                        1. GPU-Based Algorithms
                                                                          1. MapReduce Frameworks
                                                                            1. Distributed Algorithms
                                                                            2. Kinetic Data Structures
                                                                              1. Moving Objects
                                                                                1. Event-Driven Simulation
                                                                                  1. Kinetic Convex Hulls
                                                                                    1. Kinetic Nearest Neighbors
                                                                                    2. Geometric Optimization
                                                                                      1. Linear Programming
                                                                                        1. Simplex Method
                                                                                          1. Interior Point Methods
                                                                                          2. Quadratic Programming
                                                                                            1. Semidefinite Programming
                                                                                              1. Geometric Applications

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                                                                                            1. Introduction to Computational Geometry