Week 1

• Meeting 1: Introduction to the course. Planar Convex Hulls. Two algorithms for computing it. Chapter 1 of Text.
• Meeting 2: Line Segment Intersection, from Section 2.1 of the text.
• Reading: Relevant portions of the text.

Week 2

• Meeting 1: Completing plane sweep algorithm for line segment intersection.
• Meeting 2: Polygon triangulations and the art gallery problem, from Section 3.1.
• Reading: Relevant portions of Chapters 2 and 3.

Week 3

• Meeting 1: Partitioning a simple polygon into y-monotone polygons
• Meeting 2: Triangulating a y-monotone polygon. Castability as an intro to linear programming.
• Reading: Chapters 3 and 4.

Week 4

• Meeting 1: Linear Programming from Chapter 4
• Meeting 2: Analysis of randomized algorithm. Intro to Min-enclosing disk, also from Chapter 4.
• Reading: Chapter 4

Week 5

• Meeting 1: Technical lemmas needed for the min-enclosing disk algorithm
• Meeting 2: Putting everything together for min-enclosing disk. Range searching from Chapter 5.
• Reading: Chapters 4 and 5

  Week 6

  • Meeting 1: Range queries in 1-dimension and k-d trees in 2-dimensions.
  • Meeting 2: Query run time on k-d trees. Range trees.
  • Reading: Chapter 5

  Week 7

  • Meeting 1: Completing discussion of range trees. Point location.
  • Meeting 2: Point location using trapezoidal decompositions -- Algorithm for constructing and querying the structure.
  • Reading: Chapter 6

  Week 8

  • Meeting 1: Point location -- analysis of space, preprocessing, and query times.
  • Meeting 2:
  • Reading: Chapters 6 and 8