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)