Lecture Slides

1. Introduction, our goals, example problems
2. Minimum Spanning Tree & Prim's algorithm
3. MST Data Structures: Graphs and Heaps
4. Approximate Metric TSP
5. Kruskal's MST, Union-Find data structures [mst.py]
6. Clustering with minimum spanning trees [Slim-tree paper]
7. Asymptotic Analysis (2 classes) [additional MIT video lecture]
8. Depth-first search & Breadth-first search
9. Bipartite Testing & Topological Sort
10. Dijkstra's Algorithm for Shortest Paths
11. A* search algorithm & TSP [Example A* Run] [Example Dijkstra Run]
12. Bellman-Ford: Shortest Paths with Negative Weights
13. Divide & Conquer and Counting Inversions
14. Closest Points in the Plane
15. Matrix Multiplication via Strassen's Algorithm (and Karatsuba's integer multiplication)
16. Splay trees (2 classes) [demo]
17. Dynamic Programming: Subset Sum
18. Sequence Alignment [demo]
19. RNA Folding
20. Segmented Least Squared, Matrix Chain Multiplication, Optimal Binary Search Trees [extra example dynamic programming problems]
21. Linear space sequence alignment
22. Suffix Trees (2 classes)
23. Network Flow & Max-flow/mincut (2 classes)
24. Matching
25. Image segmentation
26. Extensions to network flow & Airline Scheduling
27. Linear Programming
28. P, NP, and NP-hardness reductions (3 classes)
29. NP-hardness results (3SAT, Hamiltonian path, TSP, coloring)
30. More NP-hardness proofs (3DM)
31. Randomized algorithms: Metropolis and Global Minimum Cut
32. Randomized closest pair of points
33. Class Summary