Lect  Date  Topic  Reference 
Geometric Fundamentals 
1 
08/30 
Introduction, models 
[PS P.1935] 
Geometric Data Structures I 
2 
09/01 
1D Data structures: segment, interval, and priority trees

[dBKOS Ch5, 11] 
3 
09/06 
2D orthogonal range searching, kd trees 
[dBKOS Ch5; GO Ch36] 
4 
09/08 
quad trees, range trees, Planar point location 
[dBKOS Ch5; Ch6] 
Intersection Detection 
5 
09/13 
Intersection detection: sweepline, RIC 
[dBKOS Ch2] 
6 
09/15 
RIC analysis 
[dBKOS Ch6] 
Convex Hull 
7 
09/20 
2D Convex Hull, Convex polytopes 
[PS Ch3; dBKOS Ch1; Ma Ch5] 
8 
09/22 
Convex hull in high dimensions, Guest Lecture by Thomas Mølhave 
[PS Ch3; dBKOS Ch11] 
Proximity Problems 
9 
09/27 
Voronoi Diagram, Delaunay triangulation 
[dBKOS Ch7] 

09/29 
No class 

10 
10/04 
RIC for DT, generalizations of DT 
[dBKOS Ch9; Ed P.917] 
11 
10/06 
Applications of VD/DT 
[Ed 917] 
12 
10/12 
Quad trees, WSPD 
[HP, Ch 2,3] 
13 
10/13 
WSPD, Nearest neighbor searching 
[HP Ch 3,11] 
Arrangements 
14 
10/18 
Arrangements of lines & curves, lower envelopes, zone theorem 
[dBKOS Ch8] 
15 
10/20 
Lower envelope, single cell, motion planning 
[Mat Ch 6,7; AS] 
Triangulations 
16 
10/25 
Pointset triangulation, Delaunay refinement 
[Ed Ch2] 
Geometric Sampling 
17 
10/27 
Random sampling, enets, eapproximations 
[PA Ch16] 
18 
11/01 
Geometric summaries, core sets 
[HP; AHV] 
Geometric Data Structures II 
19 
11/03 
Geometric cuttings 
[Ma Ch4 & 6] 
20 
11/08 
Simplex range searching 
[dBKOS Ch16] 
21 
11/10 
Halfspace range reporting 
[CGL] 
Geometric Optimization 
22 
11/15 
Linear programming, prune and search, RI algorithm 
[Clarkson] 
23 
11/17 
Geometric set cover 
[Clarkson] 
24 
11/22 
Shape matching 

25 
11/29 
Clustering 

Dimension Reduction 
26 
12/01 
Embedding techniques 
[Ma Ch15] 