CS 6050 Computational Geometry, Spring 2009

• Time and place: Mon Wed Fri 10:30am - 11:20am, Main 207
• Course website: http://www.cs.usu.edu/~mjiang/cs6050/spring2009/
• Professor: Dr. Minghui Jiang
  • Contact: mjiang at cc.usu.edu, 435-797-0347
  • Office hours: Mon Wed Fri 11:30am - 12:30pm, Main 402G
• Textbook: M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications, 2nd or 3rd Edition, Springer-Verlag.
• Course goals: The student will
  • Gain knowledge on a variety of computational and mathematical problems in discrete geometry and their applications.
  • Be able to utilize fundamental geometric data structures and algorithmic design techniques for the solution of new computational problems in discrete geometry.
  • Be able to implement basic geometric algorithms using standard programming languages.
  • Be prepared for theoretical research in discrete and computational geometry.
• Preparation: This is an advanced graduate-level course on discrete and computational geometry. Solid mathematical, algorithmic, and programming skills are required. The students are expected to explore the vast literatures of the field and work on current research problems under the guidance of the instructor. Prerequisite: CS5050.
• Grading:
  • Homework (25%):
    • Homework 1 (due at the beginning of class on Mon Jan 12): Read Chapter 1 and handout. Solve Exercise 1.4 on triangle pqr.
  • Project (75%):
    • Project 1 (due Fri Jan 30): Convex hull.
    • Project 2 (due Wed Mar 4): Triangulation.
    • Final Project (proposal due Mon Mar 30): Topic of your choice on maximum independent set in geometric intersection graphs.
• Resources:
  • Journals: CGTA IJCGA DCG
  • Conferences: SoCG CCCG
  • Papers:
    • T.M. Chan. Optimal output-sensitive convex hull algorithms in two and three dimensions. Discrete & Computational Geometry, 16:361-368, 1996.
    • P. Erdos and G. Szekeres. A combinatorial problem in geometry. Compositio Mathematica, 2:463-470, 1935.
• Lectures (schedule subject to change): holidays in [brackets]; important dates in red; unusual dates in blue.
  • Jan 5 7 9: Introduction. Convex hull: implementation; Graham scan, merge-hull, quick-hull; incremental construction.
  • Jan 12 14 16: Convex hull: lower bound, reduction from sorting. Chan's algorithm: binary search, partitioning, doubling search.
  • Jan [19] 21 23: Erdos and Szekeres. Pigeonhole principle.
  • Jan 26 28 30: Ordinary line. Duality (sections 8.2, 8.3). Halfplane intersection (section 4.2). Smallest enclosing circle: randomized incremental algorithm and backward analysis (section 4.7).
  • Feb 2 4 6: Euler's formula. Art gallery theorem (section 3.1). Delaunay triangulation (sections 9.1, 9.2).
  • Feb 9 11 13: Delaunay triangulation (sections 9.3, 9.4).
  • Feb 17 18 20: All things considered: Delaunay triangulation, Voronoi diagram, convex hull, and half-space intersection (sections 7.1, 8.2, 8.5, 9.2, 11.1, 11.4, 11.5).
  • Feb 23 25 27: Maximum independent set in general graphs.
  • Mar 2 4 6:
  • Mar [9 11 13]: Spring Break.
  • Mar 16 18 20: Maximum independent set in box intersection graphs.
  • Mar 23 25 27: Maximum independent sets in 2-interval graphs.
  • Mar 30 Apr 1 3:
  • Apr 6 8 10: Maximum independent sets in disk intersection graphs.
  • Apr 13 15 17:
  • Apr 20 22 24: Final project demonstration.
• Registration policy:
  • The last day to add this class is January 26.
  • The last day to drop this class without notation on your transcript is January 26.
  • Attending this class beyond January 26 without being officially registered will not be approved by the Dean's Office. Students must be officially registered for this course. No assignments or tests of any kind will be graded for students whose names do not appear on the class list.
• Code of conduct:
  • Every student should read and follow the department code of conduct.
  • Students are encouraged to discuss and exchange ideas on homework and projects, but each student must write up the solutions independently.
  • Students who are caught cheating immediately receive "Fail" grades (the instructor is absolutely firm on this policy; he has previously given two "Fail" grades for this reason).
• DRC statement: Students with physical, sensory, emotional or medical impairments may be eligible for reasonable accommodations in accordance with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973. All accommodations are coordinated through the Disability Resource Center (DRC) in Room 101 of the University Inn, 797-2444 voice, 797-0740 TTY, or toll free at 1-800-259-2966. Please contact the DRC as early in the semester as possible. Alternate format materials (Braille, large print or digital) are available with advance notice.