Planned Lecture Topics W 2008
Note: topics are still a bit under construction.
1. 1/7/08. Introduction, applications: beam/factory optimization; difference equations
2. 1/9/08 most reliable paths, expected analysis of Dijkstra (handout on main web page)
3. 1/11 reduced arc costs: removing negative arcs; euclidean shortest path
4. 1/14 Network Flow applications: arc Lower Bounds, Finding a Feasible flow with Lower bounds ().
5. 1/16 matrix rounding, project selection (KT 7.11), node connectivity
6 1/18 Scheduling on multiple processors with release times and deadlines,
Vertex and edge connectivity.
7.1/23 Global edge connectivity, Flow Algorithms and analysis
8. 1/25 Shortest A-path algorithm: Implementation details and O(mn+ mn^2) analysis
9. 1/28 Using shortest A-path algorithm for improved times in special cases; Min-Cost flow: aps and properties (weighted bipartite matching);
10. 1/30 Min-Cost flow: properties; shortest A-path algorithm (see link main page)
11. 2/1 Min-Cost flow algorithms (summary). Aplications: k-shortest disjoint paths, bus ticket allocation
12. 2/4 non-bipartite matching (summary) and applications to TSP approximation (3.2.1),
13. 2/6 Hard Problems, reductions, implications of NP-hardness (8.3),
TSP is hard to approximate (3.2)
14. 2/8 Strong NP-completeness, polynomial approximation schemes (8.3)
. 2/11 Midterm
15 2/13 Hard approximation problems: m-processor scheduling
16 2/15 Strongly NP-Hard problems:
3-partition, non-preemptive scheduling with release-times/deadlines).
Steiner trees (3.1)
17 2/20 Multi-way cuts, chapter 4.1
18 2/20 Multi-way cuts, Gomrey-Hu Trees chapter 4.2
19 2/25 Gomorey-Hu tree construction: gusfield method, handout/link
bin Packing (On-line algorithms), NF, FF, FFD
20 2/27 Bin packing: polynomial-time approximation scheme (PTAS). (9)
21 2/29 LP related approximations: IPs, LP, duality 12
22 3/3 LP related approximations: Set cover, vertex cover, rounding
and randomized rounding (13.1, 14)
23 3/5 Branch and bound solutons (Vertex cover)
24 3/7 "good" exponential time algorithms: dynamic programming for TSP and bitonic TSP.
23 3/10 Gusfield lecture: taken from
``The Perfect Phylogeny Problem" by D. Fernandez-Baca, which is
a survey paper in the book ``Steiner Trees in Industry" and
available at
http://www.cs.iastate.edu/~fernande/pubs.html
21 minimum makespan (10)
Euclidean TSP (11)