Lecture Outline

July 25th, 2008

This is a lecture outline for the class. When appropriate, I will reference chapters and sections from the textbook (KT 3 refers to Chapter 3). This outline is subject to minor changes, but I expect that the top level topics will be covered in the corresponding order.

  1. Introduction. Administrivia. Pancake Sorting and genome rearrangement, as an example of the idea of abstractions and algorithms.
  2. Analysing recurrence relations (see Quicklinks)
  3. [KT 5] Divide & Conquer/Recursion: Mergesort, closest pair, integer multiplication
  4. [KT 5] Divide & Conquer/Recursion: FFTs
  5. [KT 6] Dynamic Programming: Interval scheduling, curve fitting, subset-sum.
  6. [KT 6] Dynamic Programming: Shortest Paths
  7. [KT 4] Greedy Algorithms: Optimality principles, examples
  8. [KT 4] Greedy Algorithms: MSTs
  9. [KT 7] Network Flows: Max flows, Ford-Fulkerson and min-cuts
  10. [KT 7] Network Flows: Faster algorithms
  11. Network Flows: Variations on a theme
  12. [KT 7] Network flows: Applications
  13. [KT 8] NP-hardness: P vs NP. “Trust, but verify”. The Cook-Levin theorem & CIRCUIT-SAT
  14. [KT 8] NP-hardness: Recap, 3SAT is NP-Complete. Reduction from Independent Set to Vertex Cover
  15. [KT 8] CLIQUE, Independent Set, Set Cover, and others
  16. [KT 11] Approximation Algorithms: Definitions, Vertex Cover.
  17. Approximation Algorithms: Vertex Cover 2-approx, Interval scheduling, Set Cover
  18. [KT 11] Approximation Algorithms: Dynamic programming and PTASs (Knapsack, and a cameo by TSP)
  19. Randomized Algorithms: Hashing
  20. [KT 13] Randomized Algorithms: Min cut
  21. Randomized algorithms: Algebraic fingerprinting
  22. [KT 13] Randomized Algorithms: Chernoff Bounds
  23. Randomized Algorithms: More examples
  24. [KT 12] Heuristic methods
  25. Zero Knowledge
  26. Quantum Computing
  27. Wrap up.

Dates for homeworks/exams: to be announced soon.

This entry was posted on Friday, July 25th, 2008 at 3:49 pm and is filed under syllabus.

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