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Computational Geometry

Computational Geometry. Instructor: Prof. Pankaj Aggarwal, Department of Computer Science and Engineering, IIT Delhi. This course covers lessons in Introduction using Basic Visibility Problems, The Maximal Points Problem, The Plane Sweep Technique and applications, Convex Hull Different Paradigms and Quickhull, Dual Transformation and Applications, Lower Bounds on Algebraic Tree Model, Point Location and Triangulation, Voronoi Diagram and Delaunay Triangulation, Randomized Incremental Construction and Random Sampling, Arrangements and Levels, Range Searching, Clustering Point Sets using Quadtrees and Applications, Epsilon-Nets VC Dimension and Applications, Shape Analysis and Shape Comparison. (from nptel.ac.in)

Lecture 37 - Geometric Set Cover


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Introduction using Basic Visibility Problems
Lecture 01 - Introduction
Lecture 02 - Visibility Problems
The Maximal Points Problem
Lecture 03 - 2D Maxima
The Plane Sweep Technique and Applications
Lecture 04 - Line Sweep Method
Lecture 05 - Segment Intersection Problem
Lecture 06 - Line Sweep: Rectangle Union
Convex Hull Different Paradigms and Quickhull
Lecture 07 - Convex Hull
Lecture 08 - Convex Hull (cont.)
Lecture 09 - Quick Hull
Lecture 10 - More Convex Hull Algorithms
Dual Transformation and Applications
Lecture 11 - Insertion of Half Planes and Duality
Lecture 12 - Insertion of Half Planes and Duality (cont.)
Lower Bounds on Algebraic Tree Model
Lecture 13 - Lower Bounds
Point Location and Triangulation
Lecture 14 - Planar Point Location
Lecture 15 - Point Location and Triangulation (cont.)
Lecture 16 - Triangulation of Arbitrary Polygon
Voronoi Diagram and Delaunay Triangulation
Lecture 17 - Voronoi Diagram: Properties
Lecture 18 - Voronoi Diagram Construction
Lecture 19 - Delaunay Triangulation
Randomized Incremental Construction and Random Sampling
Lecture 20 - Quick Sort and Backward Analysis
Lecture 21 - Generalized RIC (Randomized Incremental Construction)
Lecture 22 - Randomized Incremental Construction (cont.)
Arrangements and Levels
Lecture 23 - Arrangements
Lecture 24 - Applications of Zone Theorem and Arrangements
Lecture 25 - Arrangements (cont.)
Range Searching
Lecture 26 - Range Searching: Introduction
Lecture 27 - Orthogonal Range Searching
Lecture 28 - Priority Search Trees
Lecture 29 - Non-Orthogonal Range Searching
Lecture 30 - Range Searching: Half Plane Range Counting
Clustering Point Sets using Quadtrees and Applications
Lecture 31 - Well Separated Partitioning
Lecture 32 - Quadtrees Epsilon-WSPD (Well Separated Pair Decomposition)
Lecture 33 - Construction of Epsilon-WSPD
Lecture 34 - Construction of Epsilon-WSPD (cont.)
Epsilon-Nets, VC Dimension and Applications
Lecture 35 - Epsilon-Nets and VC Dimension
Lecture 36 - Epsilon-Nets and VC Dimension (cont.)
Lecture 37 - Geometric Set Cover
Lecture 38 - Geometric Set Cover (with Bounded VC Dimension)
Shape Analysis and Shape Comparison
Lecture 39 - Shape Representation
Lecture 40 - Shape Comparison