CS 506, Computational Geometry, Spring 2020

Instructor

• Jared Saia
• Email: "last name" at cs.unm.edu.
• Office: FEC 3120, phone: 277-5446 The best way to reach me for this class is generally via Piazza. I will check it once a day, usually around noon.
• Office Hours: 1:45-3:00pm or by appointment.
• Note: I will always be available in my office during office hours. At other times, if my door is open, feel free to come in. If the door is closed, I'm probably at work on a paper, grant or research problem. Please come by another time or make an appointment via email.

Class Info

Course Description

Text Book

Piazza Forum

• Piazza forum for this class.

Syllabus

Prereq: CS 561, CS 362 or equivalent

Homework

• HW 1
• HW 2
• HW 3

Lecture Topics

• Convex Hull
• My Convex Hull Notes
• Jeff Erickson's Notes on Convex Hull
• Convex Crepes!
• High Dimensional Convex Hull; See also Quickhull
• Duality
• My Halfplane Intersection and Convex Hull Notes
• UFL lecture notes on Duality
• U. Maryland Notes, Pages 41-44 give a good connection between convex hulls, and upper/lower envelopes, Lecture 8 gives good connection between envelopes and linear programming. Lecture 16 gives good connections between convex hulls and Voronoi diagrams, and Delaunay triangulations
• Voronoi Diagrams, Delaunay Triangulations and More Dual Transformations
• My notes on Voronoi Diagrams, Delaunay Triangulations and More Dual Transformations
• Linear Programming
• My notes on Linear Programming and High-Dimensional Convex Hulls
• Linear Programming: Gupta's notes, Lecture 17
• Higher Dimensional Spaces and Dimension Reduction
• My notes on the Johnson-Lindenstrauss Projection
• My notes on the Singular Value Decomposition
• Arora Notes on Johnson-Lindenstrauss Projection
• You can embed an arbitrary metric into Euclidean space with O(log n) distortion (via Bourgain's theorem, see also here). Then, you can use Johnson-Lidenstrauss to project onto R^d where d = O(log n).
• Arora Notes on SVD (re low-rank approximation)
• Arora Notes on SVD (Part 2)
• Convex Optimization
• My notes on Multiplicative Weights Update (MWU) and learning under uncertainty
• Survey Paper on Multiplicative Weights Update by Arora et al.
• Online Convex Optimization via MWU (Section 3.9 of the Arora survey paper)
• Arora Lecture Notes on Gradient Descent and Stochastic Gradient Descent
• Andrew Ng video on Intuition of Gradient Descent
• Another interesting video on gradient descent

Projects

• Project Deliverable: The class project should be no more than 10 pages not including bibliography and appendix; it can be 2 columns.
• More details on the class project and some project ideas are available here.
• MIT Algorithm's Projects This is a general description of how to find a good CS theory project. The specific project ideas in this class are, of course, different from our own class - if you'd like specific ideas, please talk to me.

Useful Links for this Class

• Sanjeev Arora Notes on Convex Optimization
• CS 506 - Spring 2017
• Blum, Hopcroft and Kannon Foundations of Data Science
• David Mount's Computational Geometry Notes The University of Maryland notes
• David Mount's Homework Problems The University of Maryland notes
• Suresh Venkatasubramanian's Comp. Geometry Class
• Convex Optimization Notes by Vishnoi Formal Treatment of Convex Optimization Algorithms
• MWU as Gradient Descent (Section 3):
• Convex Optimization by Boyd and Vandenberghe Particularly of interest: Section 2.3 "Operations that Preserve Convexity" ; Chapter 4 and onward discuss optimization algorithms (albeit informally, without proofs of convergence time; NB that many problems discussed (i.e. quadratic programming) are NP-Hard). See Vishnoi's notes above for a more formal treatment.