Planned and Completed Lecture Topics S 2010
Note: topics with 2010 dates are failly firm, 08 dates are still from last time
1. 3/30/10. Introduction, applications: beam/factory optimization; difference equations; most reliable paths,
2. 4/1/10 expected analysis of Dijkstra (handout on main web page)
point-to-point shortest path (think Google maps): handout on main web page
3. 4/6/10 finish point-to-point shortest path (landmarks). Network flow applications: Scheduling on multiple processors with release times and deadlines.
4. 4/8/10 Network Flow applications: Edge connectivity.
Global edge connectivity,
5. 4/13/10
Matula's algorithm for global edge connectivity. Vertex Connectivity.
6 4/15/10 Improved Flow algorithms: review shortest augmenting path algorithm, : Implementation details and O(mn+ mn^2) analysis (from 222A, section 7.4 of Kleinberg Tardos);
unit flow networks, matching networks.
7.4/20/10 Min-Cost flow: aps and properties (weighted bipartite matching);
Min-Cost flow: properties; shortest A-path algorithm
8. 4/22/10 Min-Cost flow algorithms (overview).
Aplications: k-shortest disjoint paths, ticket allocation
9. 4/27/10 Finish ticket allocation; multi-commodity Flow (summary); non-bipartite matching (overview)
10. 4/29/10 Bipartite matching properties and applications (including application to TSP approximation (3.2.1).
11. 5/4/10 Intro to Hard Problems, reductions, implications of NP-hardness (
Strong NP-completeness, polynomial approximation schemes (8.1,8.3)
12. 5/6/10
Strongly NP-Hard problems:
3-partition, non-preemptive scheduling with release-times/deadlines).
13. 5/11/10 Midterm
14. 5/13/10 Midterm solutions, Multi-way cuts, chapter 4.1 (k-cuts), 4.2 multi-way cuts. Gomorey-Hu Trees
15. 5/18/10 Linear programming: conjecture disproof (Prof. Amenta)
Steiner trees (3.1)
16 5/20 K-way cuts, Gomrey-Hu Trees (Gusfield method) chapter 4.2
17 5/25/10 Steiner trees (3.1)
bin Packing (On-line algorithms), NF, FF, FFD
18 5/27/10 Bin packing (chapter 9) FF, FFD,
PTAS
19 6/1/10 Bin packing: Hard to approximate better than 3/2 (9.2),
lower bound for online algorithms,
LP related approximations: Set cover, vertex cover, rounding
and randomized rounding (13.1, 14)
20 6/3/10 Randomized rounding, set cover (more details), TSP algorithms (11)
21 2/29 LP related approximations: IPs, LP, duality 12
22 3/3
Euclidean TSP (11)
24 3/7 "good" exponential time algorithms: dynamic programming for TSP and bitonic TSP.
21 minimum makespan (10)