CS 122 Fall 2010

Running Course Outline

1. Outline of Sept. 24 class: Intro to course, Complexity rules of the road (see
handout on the class website). 

See the first supplemental video  on the past video lectures for a lecture on this material.

2. Sept. 27: big-oh, omega and theta notation. Description of Mergesort and Merge
and the start of their time analysis. Algorithm Merge is proved correct by induction
on the sum of the sizes of the two lists. The worst-case number of comparisons in
algorithm Merge on two lists of total size n is n-1 (why?).

3. Sept. 29: Worst case analysis of MergeSort by setting up a recurrence relation
and solving it by unwrapping.

4. Oct. 1: Solving a more complex recurrence relation by unwrapping. Introduction
to the problem of counting the number of inversions in a permutation.

5. Oct. 4. Counting the number of inversions in a permutation. Introduction to
fast integer multiplication by divide and conquer.

6. Oct. 6. Finished the discussion of integer multiplication by divide and conquer.
Started the discussion of randomized Selection, which will lead to randomized quicksort.

7. Oct. 8. More on randomized selection, setting up the analysis problem, random variables,
expected value (mean), partial derivation of the mean of a geometric distribution.

8. Oct. 11 Complete analysis of the expected number of comparisons in the randomized version
of Select(S,k) as a function of |S| = n. The expected number is at most 8|S| = O(n)

9. Oct. 13 Start of discussion of greedy algorithms. We looked at the problem of picking
the largest number of non-overlapping intervals.

10. Oct. 15 Dijkstra's algorithm for shortest paths in a graph with non-negative edge weights.

11. Oct. 18 Start of discussion of the minimum spanning tree problem. Prim's algorithm and
proof of correctness and running time. Kruskal's algorithm.

12. Oct. 20 proof of correctness of Kruskal's algorithm. Return to scheduling problems -
classroom scheduling problem, algorithm and correctness.

13. Oct. 22 Introduction to recursive programming and  memoization through the problem of
computing the maximum weight set of pairwise non-overlapping intervals.

14. Oct. 25 midterm

15. Oct. 27 review of memoization, introduction to dynamic programming in the weighted interval 
problem. traceback in DP.

16. Oct. 29 introduction to the RNA folding problem and recurrences for it.

17. Nov. 1 dynamic programming for RNA folding.

18. Nov. 3 dynamic programming for the shortest path problem in a weighted directed graph. 

19. Nov. 5 Floyd-Warshal algorithm for computing the shortest path in a weighted graph, between each
pair of nodes in the graph.

20. Nov. 8. The unique-decypherability problem. Definitions and start of algorithm.

21. Nov. 10 Unique-decypherability - algorithm, proof of correctness.

22. Nov. 12 Linear-time pattern matching. Z-values and Z-algorithm.

23. Nov. 15 Linear-time pattern matching. Z-values and Z-algorithm.

24. Nov. 17 Approximation Algorithms - definition, example of a factor of two approximation algorithm -   center cover problem.

25. Nov. 19 Approximation Algorithms - factor of two approximation to the vertex cover problem.

26. Nov. 22 Introduction to P and NP and poly-time reductions

27. Nov. 24 An intuitive view of NP - not the correct formal definition

28. Nov. 26 thanksgiving holiday

29. Nov. 29 Correct, formal definitions of P and NP, ending with a fast definition of NP-complete problems (languages)

30. Dec. 1 The major theorems of NP-completeness, P = NP question, the mechanics of how to prove a new problem is NP-complete.

31. Dec. 3 Dealing with NP-complete problems - approximation algorithms, fast algorithms for subsets of the whole set of problem
instances, reducing the growth rate of exponential-time solutions. A DP algorithm for the Traveling Salesman problem for n cities that
runs in O(n^2 x 2^n) time, instead of the more naive method that would take theta(n!) time.