Outline for Spring 2009

things:

problems:

how:

Lecture plan

CH: 2 lectures (graham/andrew, jarvis, chan magic, randomized IC, upper bound theorem)
CH
Projective duality: arrangements and zone theorem proof.
line segment intersection and line sweep
Voronoi (d&c) ?
Delaunay
Delaunay (relation to convex hulls)
point location, trapezoidal decomposition (RIC)
1D/2D range searching, KD trees
interval trees, segment trees
Quad trees
Meta-range searching (space-time tradeoffs, dynamization)
linear programming I
linear programming II
interlude: combinatorics of levels and lower envelopes. DS sequences.
interlude I: lower bounds
interlude II: more lower bounds
VC-dimension
eps-nets and approximations
random sampling/clarkson
cuttings
greedy reweighting
App I: art gallery
App II: Shape Matching
App III: path planning and minkowski sums
App IV: surface reconstruction

2 lectures on convex hull in 2D
- Lec 1: introduction, convexity, graham scan, jarvis march (incremental algorithms, output sensitivity)
- Lec 2: Chan's algorithm. 3D convex hull (RIC), the upper bound theorem ( $O(n^{\lceil d/2 \rceil})$ ). (the importance of counting in geometry, randomized incremental construction?)
- Assignment Q: convex hull of simple polygon in $O (n)$ time.
- Assignment Q: show that a bad incremental insertion leads to quadratic time for graham scan.
1 lecture on arrangements and duality
2 lectures on voronoi/delaunay
2 lecture on point location/trapezoidal decomposition.
1 lecture on interval trees
1 lecture on orthogonal range searching
1 lecture on partition trees and simplex range searching.
1 lecture on low-dimensional linear programming
2 lectures on eps-nets, VC-dimension, cuttings, and range searching.

Total = 13

Total = 1

Total = 4