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)