CPS 234: Course Synopsis
- Models of computation and lower bound techniques:
Various models of computation, algebraic decision
trees, Ben-Or's theorem and its extensions.
- Algorithmic paradigms and geometric transforms:
Divide and conquer, sweep-line, locus, duality,
inversion.
- Storing and searching orthogonal objects:
Segment tree, interval tree, range tree, priority
search tree, quad tree, orthogonal range
searching.
- Convex hulls: Planar convex hulls,
Graham's scan, output-sensitive algorithms,
dynamic algorithms,
higher dimensional convex hulls, randomized
algorithms, applications of convex hulls.
- Planar point location: Slab method, Kirkpatrick's
algorithm, Sarnak-Tarjan algorithm, fractional cascading,
point location in higher
dimensions.
- Arrangements: Arrangements of lines,
applications, sweep line algorithm, incremental
algorithm, zone theorem, arrangements of
hyperplanes and of simplices, lower envelope.
- Proximity problems: Closest pair, nearest neighbor, Voronoi
diagram, generalized Voronoi diagrams.
- Linear programming: Megiddo's algorithm,
randomized algorithms, parametric searching.
- Range searching: Half-plane range searching,
Ham-Sandwich theorem, partition trees, epsilon-nets, lower
bounds
- Motion planning: Configuration space, Minkowski
sum, translational motion planning, shortest paths,
nonholonomic motion planning.
- Graphics related problems: Hidden surface removal,
binary space partition, ray tracing, surface simplification,
n-body problem.
Agarwal's Home Page
CPS 234 Homepage.
Pankaj Kumar Agarwal
Fri Nov. 1 1996