CS 506 Class Syllabus

Course Web Page

Contact Info for Instructor, office hours, assignments and general information is all on the course web page.

Course Description

This course will cover topics in Geometric and Probabilistic methods in Computer Science, with an eye towards interesting, modern applications of these tools.

Text:

We will primarily use the following book and two survey papers

Computational Geometry by Mark de Berg et al.
The Multiplicative Weights Update Method: a Meta Algorithm and Applications by Arora et al.
Advanced Algorithm Design by Sanjeev Arora

A good reference book is also Probability and Computing by Mitzenmacher and Upfal.

What you should know

You should have a basic familiarity with algorithms and data structures as from a class such as CS361/CS362. You should also have a certain mathematical maturity and familiarity with proof techniques similar to what would be covered in a advanced undergraduate mathematics class. Students completing CS362, CS561, CS530 or CS500 should be well-prepared for the class. If you haven't taken any of these classes and are still interested, please come talk to me.

Topics

Topics we cover will likely include some subset of the following:

Computational Geometry
- Fundamental Problems and Algorithms: Convex Hull, Voronoi diagrams, Planar subdivisions, Triangulation
- Linear Programming and Applications
- Vector Spaces and Applications, particularly to coding theory
- Data Structures: Interval Trees, Priority Search Trees
Probability and Randomized Algorithms
- Machine Learning: Multiplicative Weights, Applications of Multiplicative Weights to Computational Geometry and Genetic Algorithms, Expert Learning
- Randomization in closest point queries, with connections to PAC learning and VC dimensions
- Randomized distributed algorithms: Maximal Independent Set, Byzantine consensus, Leader Election
- Error-correcting codes, with a focus on probabilistic and geometric methods

This class will be fairly student-driven so there is the possibility of covering other topics. Grading will be based on participation and a class project, with some (likely ungraded) homeworks to practice concepts in the class.

Course Assessment

Approximate weighting:

Homeworks 50% (3)
Class Project, 30%
General Participation, 20%.